Finite Group Databasebeta

← Group #10858852

Character table — Group #10858852

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
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-200002222222222222222-2-2-2-200000000000000-2-2-2-20000-2-200000000-2-2000000000000000000
χ182222222222222-2-2-2-22222222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000022220000-2-20000000022000000000000000000
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
χ20222222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2111111-1-11111-1-1-1-111000000000000000000
χ21222222222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2-2-222-1-11111-1-111111111-1-1000000000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1111111112222-2-2-2-211-1-1-1-1-1-1-1-1-1-1111111000000000000000000
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−i3i3i3i3i3000000-2-211−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−i3000000-2-211i3i3−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−i3i3i3i3i300000022-1-1i3i3−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−i300000022-1-1−i3−i3i3i311−i3−i3i3i3i3i3−i3−i3-1-1000000000000000000
χ2722222222-2-2-2-22-2-2-2-2222222222000022-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000002-2-2-20000220000000022000000000000000000
χ2822222222-2-2-2-22-2-2-2-22222222220000-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000-222200002200000000-2-2000000000000000000
χ2922222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-22-1-1-1-1-1-1111111111111000000000000000000
χ3022222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-22222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-22-211111111-1-1-1-11111-1-1000000000000000000
χ3122222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-11111-1-1-1-111111111-2-22222-22-1-1111111-1-1-1-1-1-1-1-111000000000000000000
χ3222222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-11111111122-2-2222-211-1-1-1-1111111-1-1-1-1-1-1000000000000000000
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−i3i3i3i3i30000002-211−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i3-1-1000000000000000000
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−i30000002-211i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i3-1-1000000000000000000
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−i3i3i3i3i3000000-22-1-1i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i311000000000000000000
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−i3000000-22-1-1−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i311000000000000000000
χ372222-2-2-2-222-2-2222-2-22-2-2-222-22-20000000022-2-20000000022-2-2000000002-22-20000002-22-22-22-22-2000000000000000000000000
χ382222-2-2-2-222-2-2222-2-22-2-2-222-22-20000000022-2-20000000022-2-200000000-22-22000000-22-222-2-22-22000000000000000000000000
χ392222-2-2-2-222-2-22-2-2222-2-2-222-2-222i2i−2i−2i000022-2-200000000-2-2222i2i−2i−2i2i2i−2i−2i00002i−2i00000000-2200002i−2i2i−2i00000000000000000000
χ402222-2-2-2-222-2-22-2-2222-2-2-222-2-22−2i−2i2i2i000022-2-200000000-2-222−2i−2i2i2i−2i−2i2i2i0000−2i2i00000000-220000−2i2i−2i2i00000000000000000000
χ412222-2-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-11133−3−333−3−3-1-11133−3−3−3−3332-22-200003−3-11-11-11-11-113−3−333−3000000000000000000
χ422222-2-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-11133−3−333−3−3-1-111−3−33333−3−3-22-2200003−31-11-1-111-11-1−333−33−3000000000000000000
χ432222-2-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-111−3−333−3−333-1-11133−3−3−3−333-22-220000−331-11-1-111-11-13−3−33−33000000000000000000
χ442222-2-2-2-222-2-2-122-2-2-1111-1-112-200000000-1-111−3−333−3−333-1-111−3−33333−3−32-22-20000−33-11-11-11-11-11−333−3−33000000000000000000
χ452222-2-2-2-222-2-2-1-2-222-1111-1-11-222i2i−2i−2i0000-1-11133−3−333−3−311-1-1−i−iii−i−iii00002i−2i00−33−i3i3i3−i31-1−i3i3i3−i3−ii−ii−33000000000000000000
χ462222-2-2-2-222-2-2-1-2-222-1111-1-11-222i2i−2i−2i0000-1-111−3−333−3−33311-1-1−i−iii−i−iii00002i−2i003−3i3−i3−i3i31-1i3−i3−i3i3−ii−ii3−3000000000000000000
χ472222-2-2-2-222-2-2-1-2-222-1111-1-11-22−2i−2i2i2i0000-1-11133−3−333−3−311-1-1ii−i−iii−i−i0000−2i2i00−33i3−i3−i3i31-1i3−i3−i3i3i−ii−i−33000000000000000000
χ482222-2-2-2-222-2-2-1-2-222-1111-1-11-22−2i−2i2i2i0000-1-111−3−333−3−33311-1-1ii−i−iii−i−i0000−2i2i003−3−i3i3i3−i31-1−i3i3i3−i3i−ii−i3−3000000000000000000
χ492222-2-2-2-2-2-222222-2-22-2-2-222-2-2200000000-2-2220000000022-2-2000000002-2-220000002-22-2-22-22-22000000000000000000000000
χ502222-2-2-2-2-2-222222-2-22-2-2-222-2-2200000000-2-2220000000022-2-200000000-222-2000000-22-22-222-22-2000000000000000000000000
χ512222-2-2-2-2-2-2222-2-2222-2-2-222-22-22i2i−2i−2i0000-2-22200000000-2-2222i2i−2i−2i2i2i−2i−2i0000−2i2i000000002-20000−2i2i−2i2i00000000000000000000
χ522222-2-2-2-2-2-2222-2-2222-2-2-222-22-2−2i−2i2i2i0000-2-22200000000-2-222−2i−2i2i2i−2i−2i2i2i00002i−2i000000002-200002i−2i2i−2i00000000000000000000
χ532222-2-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-133−3−3−3−333-1-11133−3−3−3−3332-2-2200003−3-11-111-11-11-1−333−3−33000000000000000000
χ542222-2-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-133−3−3−3−333-1-111−3−33333−3−3-222-200003−31-11-11-1-11-113−3−33−33000000000000000000
χ552222-2-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-1−3−33333−3−3-1-11133−3−3−3−333-222-20000−331-11-11-1-11-11−333−33−3000000000000000000
χ562222-2-2-2-2-2-222-122-2-2-1111-1-11-220000000011-1-1−3−33333−3−3-1-111−3−33333−3−32-2-220000−33-11-111-11-11-13−3−333−3000000000000000000
χ572222-2-2-2-2-2-222-1-2-222-1111-1-112-22i2i−2i−2i000011-1-133−3−3−3−33311-1-1−i−iii−i−iii0000−2i2i00−33−i3i3i3−i3-11i3−i3−i3i3i−ii−i3−3000000000000000000
χ582222-2-2-2-2-2-222-1-2-222-1111-1-112-22i2i−2i−2i000011-1-1−3−33333−3−311-1-1−i−iii−i−iii0000−2i2i003−3i3−i3−i3i3-11−i3i3i3−i3i−ii−i−33000000000000000000
χ592222-2-2-2-2-2-222-1-2-222-1111-1-112-2−2i−2i2i2i000011-1-133−3−3−3−33311-1-1ii−i−iii−i−i00002i−2i00−33i3−i3−i3i3-11−i3i3i3−i3−ii−ii3−3000000000000000000
χ602222-2-2-2-2-2-222-1-2-222-1111-1-112-2−2i−2i2i2i000011-1-1−3−33333−3−311-1-1ii−i−iii−i−i00002i−2i003−3−i3i3i3−i3-11i3−i3−i3i3−ii−ii−33000000000000000000
χ6122-2-22-2-222-22-22000022-2-2-2-220000002i−2i2i−2i2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000022−2−222−2−20000−i2i2−i2i200
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χ944-4-4444-4-40000-2-44-4422-222-2-200000000000000000000002-22-2−2i32i3−2i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000
χ954-4-4444-4-40000-2-44-4422-222-2-200000000000000000000002-22-22i3−2i32i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000
χ964-4-44-4-444000044-4-44-44-44-44-400000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ974-4-44-4-4440000-24-4-442-22-22-220000000000000000000000-222-223−23−2323−232323−2300000000000000000000000000000000000000000000
χ984-4-44-4-4440000-24-4-442-22-22-220000000000000000000000-222-2−232323−2323−23−232300000000000000000000000000000000000000000000
χ994-4-44-4-4440000-2-444-42-22-22-22004i−4i−4i4i00000000000000002-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000000000
χ1004-4-44-4-4440000-2-444-42-22-22-2200−4i4i4i−4i00000000000000002-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000
χ1018-88-88-88-80000-40000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-88-880000-400004-4-44-444000000000000000000000000000000000000000000000000000000000000000000000000000000

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