Finite Group Databasebeta

← Group #10858792

Character table — Group #10858792

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order12222222222234444666666644444444446666121212121212121212121212121212121212121244444444121212121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11111-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11111-111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-200002222222222222222-2-2-2-200000000-2000000-2-2-20000-2-200000000-2-2000000000000000000
χ182222222222222-2-2-2-22222222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000020000002220000-2-20000000022000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-2111111-1-11111-1-1-1-111000000000000000000
χ21222222222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111112-2-2-2-2-2-22-1-11111-1-111111111-1-1000000000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-111111111-22222-2-2-211-1-1-1-1-1-1-1-1-1-1111111000000000000000000
χ23222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-200002222-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-2000000-211−i3−i3i3i311−i3−i3i3i3−i3−i3i3i311000000000000000000
χ24222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-200002222-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-2000000-211i3i3−i3−i311i3i3−i3−i3i3i3−i3−i311000000000000000000
χ25222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i320000002-1-1i3i3−i3−i311i3i3−i3−i3−i3−i3i3i3-1-1000000000000000000
χ26222222222222-1-2-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i320000002-1-1−i3−i3i3i311−i3−i3i3i3i3i3−i3−i3-1-1000000000000000000
χ2722222222-2-2-2-22-2-2-2-2222222222000022-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000002000000-22200002200000000-2-2000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222220000-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000-20000002-2-20000220000000022000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-222-2-2211111111-1-1-1-11111-1-1000000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-22222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-11111-1-1-1-111111111-222-2-222211-1-1-1-1111111-1-1-1-1-1-1000000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-1111111112-2-22222-2-1-1111111-1-1-1-1-1-1-1-111000000000000000000
χ3322222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122000022-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i32000000-2-1-1i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i311000000000000000000
χ3422222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-122000022-2-21111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i32000000-2-1-1−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i311000000000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-2000000211−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i3-1-1000000000000000000
χ3622222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-2000000211i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i3-1-1000000000000000000
χ3722-222-2-2-222-2-2222-2-22-2-2-222-22-20000000022-2-20000000022-2-20000000002-22-2000002-22-22-22-22-2000000000000000000000000
χ3822-222-2-2-222-2-2222-2-22-2-2-222-22-20000000022-2-20000000022-2-2000000000-22-2200000-22-222-2-22-22000000000000000000000000
χ3922-222-2-2-222-2-22-2-2222-2-2-222-2-222i2i−2i−2i000022-2-200000000-2-2222i2i−2i−2i2i2i−2i−2i000002i−2i0000000-2200002i−2i2i−2i00000000000000000000
χ4022-222-2-2-222-2-22-2-2222-2-2-222-2-22−2i−2i2i2i000022-2-200000000-2-222−2i−2i2i2i−2i−2i2i2i00000−2i2i0000000-220000−2i2i−2i2i00000000000000000000
χ4122-222-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-11133−3−333−3−3-1-11133−3−3−3−33302-22-20003−3-11-11-11-11-113−3−333−3000000000000000000
χ4222-222-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-11133−3−333−3−3-1-111−3−33333−3−30-22-220003−31-11-1-111-11-1−333−33−3000000000000000000
χ4322-222-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-111−3−333−3−333-1-11133−3−3−3−3330-22-22000−331-11-1-111-11-13−3−33−33000000000000000000
χ4422-222-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-111−3−333−3−333-1-111−3−33333−3−302-22-2000−33-11-11-11-11-11−333−3−33000000000000000000
χ4522-222-2-2-222-2-2-1-2-222-1111-1-11-222i2i−2i−2i0000-1-11133−3−333−3−311-1-1−i−iii−i−iii000002i−2i0−33−i3i3i3−i31-1−i3i3i3−i3−ii−ii−33000000000000000000
χ4622-222-2-2-222-2-2-1-2-222-1111-1-11-222i2i−2i−2i0000-1-111−3−333−3−33311-1-1−i−iii−i−iii000002i−2i03−3i3−i3−i3i31-1i3−i3−i3i3−ii−ii3−3000000000000000000
χ4722-222-2-2-222-2-2-1-2-222-1111-1-11-22−2i−2i2i2i0000-1-11133−3−333−3−311-1-1ii−i−iii−i−i00000−2i2i0−33i3−i3−i3i31-1i3−i3−i3i3i−ii−i−33000000000000000000
χ4822-222-2-2-222-2-2-1-2-222-1111-1-11-22−2i−2i2i2i0000-1-111−3−333−3−33311-1-1ii−i−iii−i−i00000−2i2i03−3−i3i3i3−i31-1−i3i3i3−i3i−ii−i3−3000000000000000000
χ4922-222-2-2-2-2-222222-2-22-2-2-222-2-2200000000-2-2220000000022-2-20000000002-2-22000002-22-2-22-22-22000000000000000000000000
χ5022-222-2-2-2-2-222222-2-22-2-2-222-2-2200000000-2-2220000000022-2-2000000000-222-200000-22-22-222-22-2000000000000000000000000
χ5122-222-2-2-2-2-2222-2-2222-2-2-222-22-22i2i−2i−2i0000-2-22200000000-2-2222i2i−2i−2i2i2i−2i−2i00000−2i2i00000002-20000−2i2i−2i2i00000000000000000000
χ5222-222-2-2-2-2-2222-2-2222-2-2-222-22-2−2i−2i2i2i0000-2-22200000000-2-222−2i−2i2i2i−2i−2i2i2i000002i−2i00000002-200002i−2i2i−2i00000000000000000000
χ5322-222-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-133−3−3−3−333-1-11133−3−3−3−3330-222-2000−331-11-11-1-11-11−333−33−3000000000000000000
χ5422-222-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-133−3−3−3−333-1-111−3−33333−3−302-2-22000−33-11-111-11-11-13−3−333−3000000000000000000
χ5522-222-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-1−3−33333−3−3-1-11133−3−3−3−33302-2-220003−3-11-111-11-11-1−333−3−33000000000000000000
χ5622-222-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-1−3−33333−3−3-1-111−3−33333−3−30-222-20003−31-11-11-1-11-113−3−33−33000000000000000000
χ5722-222-2-2-2-2-222-1-2-222-1111-1-112-22i2i−2i−2i000011-1-133−3−3−3−33311-1-1−i−iii−i−iii00000−2i2i03−3i3−i3−i3i3-11−i3i3i3−i3i−ii−i−33000000000000000000
χ5822-222-2-2-2-2-222-1-2-222-1111-1-112-22i2i−2i−2i000011-1-1−3−33333−3−311-1-1−i−iii−i−iii00000−2i2i0−33−i3i3i3−i3-11i3−i3−i3i3i−ii−i3−3000000000000000000
χ5922-222-2-2-2-2-222-1-2-222-1111-1-112-2−2i−2i2i2i000011-1-133−3−3−3−33311-1-1ii−i−iii−i−i000002i−2i03−3−i3i3i3−i3-11i3−i3−i3i3−ii−ii−33000000000000000000
χ6022-222-2-2-2-2-222-1-2-222-1111-1-112-2−2i−2i2i2i000011-1-1−3−33333−3−311-1-1ii−i−iii−i−i000002i−2i0−33i3−i3−i3i3-11−i3i3i3−i3−ii−ii3−3000000000000000000
χ6122-2-2-2-2222-22-220000222-2-2-2-20000002-22-22-22-22-22-22-22-200000000000000000000000000000000000000−i2−i2i2i2−i2−i2i2i20000−i2i2−i2i200
χ6222-2-2-2-2222-22-220000222-2-2-2-20000002-22-22-22-22-22-22-22-200000000000000000000000000000000000000i2i2−i2−i2i2i2−i2−i20000i2−i2i2−i200
χ6322-2-2-2-2222-22-220000222-2-2-2-2000000-22-222-22-2-22-22-22-2200000000000000000000000000000000000000−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i200
χ6422-2-2-2-2222-22-220000222-2-2-2-2000000-22-222-22-2-22-22-22-2200000000000000000000000000000000000000i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i200
χ6522-2-2-2-222-22-2220000222-2-2-2-20000002-2-22-22-222-22-2-22-2200000000000000000000000000000000000000−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i200
χ6622-2-2-2-222-22-2220000222-2-2-2-20000002-2-22-22-222-22-2-22-2200000000000000000000000000000000000000i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i200
χ6722-2-2-2-222-22-2220000222-2-2-2-2000000-222-2-22-22-22-222-22-200000000000000000000000000000000000000−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i200
χ6822-2-2-2-222-22-2220000222-2-2-2-2000000-222-2-22-22-22-222-22-200000000000000000000000000000000000000i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i200
χ692-22-22-2-22000022-22-2-22-22-22-2002i−2i2i−2i00000000000000002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000002i−2i2i−2i00002-200000000
χ702-22-22-2-22000022-22-2-22-22-22-2002i−2i2i−2i00000000000000002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000−2i2i−2i2i0000-2200000000
χ712-22-22-2-22000022-22-2-22-22-22-200−2i2i−2i2i00000000000000002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000002i−2i2i−2i0000-2200000000
χ722-22-22-2-22000022-22-2-22-22-22-200−2i2i−2i2i00000000000000002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−2i2i−2i2i00002-200000000
χ732-2-2-2222-200002-222-2-2-22-2-222002-2-220000000000000000-222-22-2-222-2-220000000000000000000000000000002i−2i2i−2i002i−2i000000
χ742-2-2-2222-200002-222-2-2-22-2-222002-2-220000000000000000-222-22-2-222-2-22000000000000000000000000000000−2i2i−2i2i00−2i2i000000
χ752-2-2-2222-200002-222-2-2-22-2-22200-222-20000000000000000-222-2-222-2-222-20000000000000000000000000000002i−2i2i−2i00−2i2i000000
χ762-2-2-2222-200002-222-2-2-22-2-22200-222-20000000000000000-222-2-222-2-222-2000000000000000000000000000000−2i2i−2i2i002i−2i000000
χ77444-4-44-4-44-4-44400004-4-44-4-4400000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ78444-4-44-4-44-4-44-20000-222-222-20000000000-222-223−23−232323−23−232300000000000000000000000000000000000000000000000000000000
χ79444-4-44-4-44-4-44-20000-222-222-20000000000-222-2−232323−23−232323−2300000000000000000000000000000000000000000000000000000000
χ80444-4-44-4-4-444-4400004-4-44-4-440000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ81444-4-44-4-4-444-4-20000-222-222-200000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000000000
χ82444-4-44-4-4-444-4-20000-222-222-200000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000000000
χ8344-4-4-4-4444-44-4-20000-2-2-222220000004-44-4-22-22-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ8444-4-4-4-4444-44-4-20000-2-2-22222000000-44-44-22-222-22-22-22-200000000000000000000000000000000000000000000000000000000
χ8544-4-4-4-444-44-44-20000-2-2-222220000004-4-442-22-2-22-222-22-200000000000000000000000000000000000000000000000000000000
χ8644-4-4-4-444-44-44-20000-2-2-22222000000-444-42-22-22-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ874-444-4-44-4000040000-4-4444-4-4000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ884-444-4-44-4000040000-4-4444-4-40000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ894-44-44-4-4400004-44-44-44-44-44-40000000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ904-44-44-4-440000-24-44-42-22-22-22004i−4i4i−4i0000000000000000-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ914-44-44-4-440000-24-44-42-22-22-2200−4i4i−4i4i0000000000000000-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ924-44-44-4-440000-2-44-442-22-22-2200000000000000000000002-22-223−2323−23−2323−232300000000000000000000000000000000000000000000
χ934-44-44-4-440000-2-44-442-22-22-2200000000000000000000002-22-2−2323−232323−2323−2300000000000000000000000000000000000000000000
χ944-4-44-44-44000040000-44-4-44-4400000000000000000000000000000000000000000000000000000000000022−22−222200000000000000
χ954-4-44-44-44000040000-44-4-44-44000000000000000000000000000000000000000000000000000000000000−222222−2200000000000000
χ964-4-4-4444-4000044-4-44-4-44-4-44400000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ974-4-4-4444-40000-24-4-4422-222-2-20000000000000000000000-222-2−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000
χ984-4-4-4444-40000-24-4-4422-222-2-20000000000000000000000-222-22i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000
χ994-4-4-4444-40000-2-444-422-222-2-2004-4-4400000000000000002-2-22-222-2-222-200000000000000000000000000000000000000000000
χ1004-4-4-4444-40000-2-444-422-222-2-200-444-400000000000000002-2-222-2-222-2-2200000000000000000000000000000000000000000000
χ1018-888-8-88-80000-4000044-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-88-880000-400004-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).