Finite Group Databasebeta

← Group #11713976

Character table — Group #11713976

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222666688888888888888888888888888888888121212121212242424242424242448484848
order122222222222444444444444366666666666666612121212121212121212121212121212444444888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ511111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11-11-1
χ611111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-11-11
χ711111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1111-1-11
χ811111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-111-1
χ9222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222000000000000
χ10222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-222000000000000
χ1122222222-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111122-2-2-2-2000000000000
χ1222222222-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-111111111-111111111-1-1-1-1-1-1-1-1-2-222-2-2000000000000
χ13222-2-2-2-2200002i2i−2i−2i00002-22-22222-2-2-200000000-22i2i2i2i−2i−2i−2i−2i000000002i−2i0000000000000000
χ14222-2-2-2-2200002i2i−2i−2i00002-22-2-1-1-1-1111−i3−i3−i3−i3i3i3i3i31−i−i−i−iiiii3333−3−3−3−32i−2i0000000000000000
χ15222-2-2-2-2200002i2i−2i−2i00002-22-2-1-1-1-1111i3i3i3i3−i3−i3−i3−i31−i−i−i−iiiii−3−3−3−333332i−2i0000000000000000
χ16222-2-2-2-220000−2i−2i2i2i00002-22-22222-2-2-200000000-2−2i−2i−2i−2i2i2i2i2i00000000−2i2i0000000000000000
χ17222-2-2-2-220000−2i−2i2i2i00002-22-2-1-1-1-1111−i3−i3−i3−i3i3i3i3i31iiii−i−i−i−i−3−3−3−33333−2i2i0000000000000000
χ18222-2-2-2-220000−2i−2i2i2i00002-22-2-1-1-1-1111i3i3i3i3−i3−i3−i3−i31iiii−i−i−i−i3333−3−3−3−3−2i2i0000000000000000
χ1922-2-222-2-222-2-22i−2i2i−2i2i2i−2i−2i0000-111-11-1-111-1-111-1-11ii−i−iii−i−iii−i−iii−i−i000000−i2i2−i2i22−22−20000
χ2022-2-222-2-222-2-22i−2i2i−2i2i2i−2i−2i0000-111-11-1-111-1-111-1-11ii−i−iii−i−iii−i−iii−i−i000000i2−i2i2−i2−22−220000
χ2122-2-222-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000-111-11-1-111-1-111-1-11−i−iii−i−iii−i−iii−i−iii000000−i2i2−i2i2−22−220000
χ2222-2-222-2-222-2-2−2i2i−2i2i−2i−2i2i2i0000-111-11-1-111-1-111-1-11−i−iii−i−iii−i−iii−i−iii000000i2−i2i2−i22−22−20000
χ2322-2-222-2-2-2-2222i−2i2i−2i−2i−2i2i2i0000-111-11-1-1-1-111-1-1111ii−i−iii−i−i−i−iii−i−iii000000−i2i2i2−i22−2−220000
χ2422-2-222-2-2-2-2222i−2i2i−2i−2i−2i2i2i0000-111-11-1-1-1-111-1-1111ii−i−iii−i−i−i−iii−i−iii000000i2−i2−i2i2−222−20000
χ2522-2-222-2-2-2-222−2i2i−2i2i2i2i−2i−2i0000-111-11-1-1-1-111-1-1111−i−iii−i−iiiii−i−iii−i−i000000−i2i2i2−i2−222−20000
χ2622-2-222-2-2-2-222−2i2i−2i2i2i2i−2i−2i0000-111-11-1-1-1-111-1-1111−i−iii−i−iiiii−i−iii−i−i000000i2−i2−i2i22−2−220000
χ272-2-222-2-22000000002-22-2-222-222-2-2-22-2000000002000000002-22-22-22-2002-200000000000000
χ282-2-222-2-22000000002-22-2-222-2-1-1111-11−i3i3−i3i3−i3i3−i3i3-1−i3i3−i3i3−i3i3−i3i3-11-11-11-11002-200000000000000
χ292-2-222-2-22000000002-22-2-222-2-1-1111-11i3−i3i3−i3i3−i3i3−i3-1i3−i3i3−i3i3−i3i3−i3-11-11-11-11002-200000000000000
χ302-2-222-2-2200000000-22-22-222-222-2-2-22-200000000200000000-22-22-22-2200-2200000000000000
χ312-2-222-2-2200000000-22-22-222-2-1-1111-11−i3i3−i3i3−i3i3−i3i3-1i3−i3i3−i3i3−i3i3−i31-11-11-11-100-2200000000000000
χ322-2-222-2-2200000000-22-22-222-2-1-1111-11i3−i3i3−i3i3−i3i3−i3-1−i3i3−i3i3−i3i3−i3i31-11-11-11-100-2200000000000000
χ332-2-2-2-22222-22-200000000-2-22222-2-22-222-22-2-22-22-2000000000000000000002-2000000000000
χ342-2-2-2-22222-22-200000000-2-222-1-111-11-1-11-111-11-113−33−3−33−333−33−3−33−3300002-2000000000000
χ352-2-2-2-22222-22-200000000-2-222-1-111-11-1-11-111-11-11−33−333−33−3−33−333−33−300002-2000000000000
χ362-2-2-2-2222-22-2200000000-2-22222-2-22-22-22-222-22-2-200000000000000000000-22000000000000
χ372-2-2-2-2222-22-2200000000-2-222-1-111-11-11-11-1-11-1113−33−3−33−33−33−333−33−30000-22000000000000
χ382-2-2-2-2222-22-2200000000-2-222-1-111-11-11-11-1-11-111−33−333−33−33−33−3−33−330000-22000000000000
χ3933333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-111111111-1-1-1-1
χ4033333333333333333333-1-1-1-100000000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41333333333333-3-3-3-3-3-3-3-3-1-1-1-1000000000000000000000000000000001111-1-11111-1-1-1-1-1-111
χ42333333333333-3-3-3-3-3-3-3-3-1-1-1-1000000000000000000000000000000001111-1-1-1-1-1-1111111-1-1
χ4333333333-3-3-3-33333-3-3-3-3-1-1-1-100000000000000000000000000000000-1-1111111-1-111-1-1-11-11
χ4433333333-3-3-3-33333-3-3-3-3-1-1-1-100000000000000000000000000000000-1-11111-1-111-1-1111-11-1
χ4533333333-3-3-3-3-3-3-3-33333-1-1-1-10000000000000000000000000000000011-1-11111-1-1-1-111-111-1
χ4633333333-3-3-3-3-3-3-3-33333-1-1-1-10000000000000000000000000000000011-1-111-1-11111-1-11-1-11
χ4744-44-4-44-400004-4-44000000001-1-111-1-1−i3−i3i3i3i3i3−i3−i31-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
χ4844-44-4-44-400004-4-44000000001-1-111-1-1i3i3−i3−i3−i3−i3i3i31-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000
χ4944-44-4-44-400004-4-4400000000-222-2-22200000000-222-2-2-2-22200000000000000000000000000
χ5044-44-4-44-40000-444-4000000001-1-111-1-1−i3−i3i3i3i3i3−i3−i3111-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000
χ5144-44-4-44-40000-444-4000000001-1-111-1-1i3i3−i3−i3−i3−i3i3i3111-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000
χ5244-44-4-44-40000-444-400000000-222-2-22200000000-2-2-22222-2-200000000000000000000000000
χ5344-4-444-4-444-4-44i−4i4i−4i4i4i−4i−4i00001-1-11-111-1-111-1-111-1−i−iii−i−iii−i−iii−i−iii000000000000000000
χ5444-4-444-4-444-4-4−4i4i−4i4i−4i−4i4i4i00001-1-11-111-1-111-1-111-1ii−i−iii−i−iii−i−iii−i−i000000000000000000
χ5544-4-444-4-4-4-4444i−4i4i−4i−4i−4i4i4i00001-1-11-11111-1-111-1-1-1−i−iii−i−iiiii−i−iii−i−i000000000000000000
χ5644-4-444-4-4-4-444−4i4i−4i4i4i4i−4i−4i00001-1-11-11111-1-111-1-1-1ii−i−iii−i−i−i−iii−i−iii000000000000000000
χ574-444-44-4-44-4-440000000000001-11-1-1-11-111-11-1-111−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ584-444-44-4-44-4-440000000000001-11-1-1-11-111-11-1-111i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ594-444-44-4-44-4-44000000000000-22-2222-22-2-22-222-2-20000000000000000000000000000000000
χ604-444-44-4-4-444-40000000000001-11-1-1-111-1-11-111-11−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000000000
χ614-444-44-4-4-444-40000000000001-11-1-1-111-1-11-111-11i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000000000
χ624-444-44-4-4-444-4000000000000-22-2222-2-222-22-2-22-20000000000000000000000000000000000
χ634-44-44-44-4000000004i−4i−4i4i00001-11-111-1−i3i3i3−i3−i3i3i3−i3-13−3−333−3−33−iii−i−iii−i000000000000000000
χ644-44-44-44-4000000004i−4i−4i4i00001-11-111-1i3−i3−i3i3i3−i3−i3i3-1−333−3−333−3−iii−i−iii−i000000000000000000
χ654-44-44-44-4000000004i−4i−4i4i0000-22-22-2-22000000002000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ664-44-44-44-400000000−4i4i4i−4i00001-11-111-1−i3i3i3−i3−i3i3i3−i3-1−333−3−333−3i−i−iii−i−ii000000000000000000
χ674-44-44-44-400000000−4i4i4i−4i00001-11-111-1i3−i3−i3i3i3−i3−i3i3-13−3−333−3−33i−i−iii−i−ii000000000000000000
χ684-44-44-44-400000000−4i4i4i−4i0000-22-22-2-2200000000200000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ69666-6-6-6-6600006i6i−6i−6i0000-22-2200000000000000000000000000000000−2i2i0000000000000000
χ70666-6-6-6-660000−6i−6i6i6i0000-22-22000000000000000000000000000000002i−2i0000000000000000
χ716-6-666-6-66000000006-66-62-2-220000000000000000000000000000000000-2200000000000000
χ726-6-666-6-6600000000-66-662-2-2200000000000000000000000000000000002-200000000000000
χ736-6-6-6-66666-66-60000000022-2-2000000000000000000000000000000000000-22000000000000
χ746-6-6-6-6666-66-660000000022-2-20000000000000000000000000000000000002-2000000000000

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