Finite Group Databasebeta

← Group #10853286

Character table — Group #10853286

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order122222223444444446666666444444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-11111111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ10111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-11111111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ11111111111-1-1-1-111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ12111111111-1-1-1-111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111111111111111-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ14111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2-22222222-2-200002222222222222222-2-2-2-200000000-2-2000000-2-2-2-2-2-2000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000220000002222-2-2000000000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222000022-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000-22000000-2-22222000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000002-200000022-2-222000000000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-21111-1-1-1-1-1-111111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-111111111-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-1000000000000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-200002222-1-1-1-1-1-1-1-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i3-2-2000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-200002222-1-1-1-1-1-1-1-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i3-2-2000000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-1-1-1111111111111−i3−i3−i3−i3i3i3i3i322000000-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-1-1-1111111111111i3i3i3i3−i3−i3−i3−i322000000-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-12-2-2-222-2-2-1-111111111-1-1-1-11111000000000000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2-2-2-22211-1-11111111111-1-1-1-1000000000000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-21111-1-1-1-11111-1-1-1-1111111112-222-2-222-1-11111-1-1-1-11111-1-1-1-1000000000000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-1-1-1-1-111111111-222222-2-211-1-111-1-1-1-1-1-1-1-11111000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000022-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3-2200000011-1-1-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000022-2-21111-1-1-1-111111111i3i3i3i3−i3−i3−i3−i3-2200000011-1-1-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i32-2000000-1-111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i32-2000000-1-111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000000000
χ3722-222-2-2-2222-2-222-2-2-22-2-222-22-222-2-2000022-2-20000000022-2-222-2-222-2-2002-2000000002-22-22-200000000000000000000000000
χ3822-222-2-2-2222-2-222-2-2-22-2-222-22-2-2-222000022-2-20000000022-2-2-2-222-2-22200-22000000002-2-22-2200000000000000000000000000
χ3922-222-2-2-2222-2-2-2-222-22-2-222-2-220000000022-2-200000000-2-2220000000000002i−2i2i−2i0000-2200002i−2i2i−2i2i−2i2i−2i000000000000000000
χ4022-222-2-2-2222-2-2-2-222-22-2-222-2-220000000022-2-200000000-2-222000000000000−2i2i−2i2i0000-220000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ4122-222-2-2-22-2-22222-2-2-22-2-222-2-2222-2-20000-2-2220000000022-2-222-2-222-2-200-2200000000-22-22-2200000000000000000000000000
χ4222-222-2-2-22-2-22222-2-2-22-2-222-2-22-2-2220000-2-2220000000022-2-2-2-222-2-222002-200000000-222-22-200000000000000000000000000
χ4322-222-2-2-22-2-222-2-222-22-2-222-22-200000000-2-22200000000-2-2220000000000002i−2i−2i2i00002-200002i−2i2i−2i−2i2i−2i2i000000000000000000
χ4422-222-2-2-22-2-222-2-222-22-2-222-22-200000000-2-22200000000-2-222000000000000−2i2i2i−2i00002-20000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ4522-222-2-2-2-122-2-222-2-21-111-1-112-222-2-20000-1-11133−3−333−3−3-1-111-1-111-1-111002-200003−33−3-11-11-113−3−333−3−33000000000000000000
χ4622-222-2-2-2-122-2-222-2-21-111-1-112-222-2-20000-1-111−3−333−3−333-1-111-1-111-1-111002-20000−33−33-11-11-11−333−3−333−3000000000000000000
χ4722-222-2-2-2-122-2-222-2-21-111-1-112-2-2-2220000-1-11133−3−333−3−3-1-11111-1-111-1-100-2200003−33−3-111-11-1−333−3−333−3000000000000000000
χ4822-222-2-2-2-122-2-222-2-21-111-1-112-2-2-2220000-1-111−3−333−3−333-1-11111-1-111-1-100-220000−33−33-111-11-13−3−333−3−33000000000000000000
χ4922-222-2-2-2-122-2-2-2-2221-111-1-11-2200000000-1-11133−3−333−3−311-1-1−i3−i3i3i3i3i3−i3−i300002i−2i2i−2i−33−331-1−i3i3i3−i3−ii−ii−ii−ii000000000000000000
χ5022-222-2-2-2-122-2-2-2-2221-111-1-11-2200000000-1-11133−3−333−3−311-1-1i3i3−i3−i3−i3−i3i3i30000−2i2i−2i2i−33−331-1i3−i3−i3i3i−ii−ii−ii−i000000000000000000
χ5122-222-2-2-2-122-2-2-2-2221-111-1-11-2200000000-1-111−3−333−3−33311-1-1−i3−i3i3i3i3i3−i3−i30000−2i2i−2i2i3−33−31-1−i3i3i3−i3i−ii−ii−ii−i000000000000000000
χ5222-222-2-2-2-122-2-2-2-2221-111-1-11-2200000000-1-111−3−333−3−33311-1-1i3i3−i3−i3−i3−i3i3i300002i−2i2i−2i3−33−31-1i3−i3−i3i3−ii−ii−ii−ii000000000000000000
χ5322-222-2-2-2-1-2-22222-2-21-111-1-11-2222-2-2000011-1-133−3−3−3−333-1-111-1-111-1-11100-2200003−3−331-11-11-13−3−33−333−3000000000000000000
χ5422-222-2-2-2-1-2-22222-2-21-111-1-11-2222-2-2000011-1-1−3−33333−3−3-1-111-1-111-1-11100-220000−333−31-11-11-1−333−33−3−33000000000000000000
χ5522-222-2-2-2-1-2-22222-2-21-111-1-11-22-2-222000011-1-133−3−3−3−333-1-11111-1-111-1-1002-200003−3−331-1-11-11−333−33−3−33000000000000000000
χ5622-222-2-2-2-1-2-22222-2-21-111-1-11-22-2-222000011-1-1−3−33333−3−3-1-11111-1-111-1-1002-20000−333−31-1-11-113−3−33−333−3000000000000000000
χ5722-222-2-2-2-1-2-222-2-2221-111-1-112-20000000011-1-133−3−3−3−33311-1-1−i3−i3i3i3i3i3−i3−i300002i−2i−2i2i−333−3-11i3−i3−i3i3−ii−iii−ii−i000000000000000000
χ5822-222-2-2-2-1-2-222-2-2221-111-1-112-20000000011-1-133−3−3−3−33311-1-1i3i3−i3−i3−i3−i3i3i30000−2i2i2i−2i−333−3-11−i3i3i3−i3i−ii−i−ii−ii000000000000000000
χ5922-222-2-2-2-1-2-222-2-2221-111-1-112-20000000011-1-1−3−33333−3−311-1-1−i3−i3i3i3i3i3−i3−i30000−2i2i2i−2i3−3−33-11i3−i3−i3i3i−ii−i−ii−ii000000000000000000
χ6022-222-2-2-2-1-2-222-2-2221-111-1-112-20000000011-1-1−3−33333−3−311-1-1i3i3−i3−i3−i3−i3i3i300002i−2i−2i2i3−3−33-11−i3i3i3−i3−ii−iii−ii−i000000000000000000
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χ954-4-44-444-4-200004-4-44-2222-22-2004i−4i−4i4i0000000000000000-222-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000000000
χ964-4-44-444-4-200004-4-44-2222-22-200−4i4i4i−4i0000000000000000-222-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000
χ974-4-44-444-4-20000-444-4-2222-22-200000000000000000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000
χ984-4-44-444-4-20000-444-4-2222-22-200000000000000000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000
χ994-4-4-444-44400000000-4-44-4-444000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ1004-4-4-444-44400000000-4-44-4-4440000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ1018-88-88-88-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8-888-88-40000000044-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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