Finite Group Databasebeta

← Group #11714044

Character table — Group #11714044

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222666688888888888888888888888888888888121212121212242424242424242448484848
order122222222222444444444444366666666666666612121212121212121212121212121212444444888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-11
χ4111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-111-1
χ511111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ611111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111
χ711111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111-11-1
χ811111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-11-11
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
χ10222222222222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2000000000000
χ1122222222-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111111111-2-222-2-2000000000000
χ1222222222-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-111111111-111111111-1-1-1-1-1-1-1-1-2-2-2-222000000000000
χ13222-2-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i0000-1111-1-1-11111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i000000−i2i2−i2i22−22−20000
χ14222-2-2-2-2222-2-22i2i−2i−2i2i2i−2i−2i0000-1111-1-1-11111-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i000000i2−i2i2−i2−22−220000
χ15222-2-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0000-1111-1-1-11111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii000000−i2i2−i2i2−22−220000
χ16222-2-2-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0000-1111-1-1-11111-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii000000i2−i2i2−i22−22−20000
χ17222-2-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i0000-1111-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii000000−i2i2i2−i22−2−220000
χ18222-2-2-2-22-2-2222i2i−2i−2i−2i−2i2i2i0000-1111-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii000000i2−i2−i2i2−222−20000
χ19222-2-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i0000-1111-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i000000−i2i2i2−i2−222−20000
χ20222-2-2-2-22-2-222−2i−2i2i2i2i2i−2i−2i0000-1111-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i000000i2−i2−i2i22−2−220000
χ2122-2-222-2-2000000002i−2i2i−2i22-2-2222-22-2-200000000-2000000002i2i−2i−2i2i2i−2i−2i00002i−2i000000000000
χ2222-2-222-2-2000000002i−2i2i−2i22-2-2-1-1-11-111−i3−i3i3i3−i3−i3i3i3133−3−333−3−3−i−iii−i−iii00002i−2i000000000000
χ2322-2-222-2-2000000002i−2i2i−2i22-2-2-1-1-11-111i3i3−i3−i3i3i3−i3−i31−3−333−3−333−i−iii−i−iii00002i−2i000000000000
χ2422-2-222-2-200000000−2i2i−2i2i22-2-2222-22-2-200000000-200000000−2i−2i2i2i−2i−2i2i2i0000−2i2i000000000000
χ2522-2-222-2-200000000−2i2i−2i2i22-2-2-1-1-11-111−i3−i3i3i3−i3−i3i3i31−3−333−3−333ii−i−iii−i−i0000−2i2i000000000000
χ2622-2-222-2-200000000−2i2i−2i2i22-2-2-1-1-11-111i3i3−i3−i3i3i3−i3−i3133−3−333−3−3ii−i−iii−i−i0000−2i2i000000000000
χ272-22-22-22-200002i−2i2i−2i00002-22-222-22-22-200000000-22i−2i2i−2i2i−2i2i−2i00000000002i−2i00000000000000
χ282-22-22-22-200002i−2i2i−2i00002-22-2-1-11-11-11−i3i3−i3i3−i3i3−i3i31−ii−ii−ii−ii3−33−33−33−3002i−2i00000000000000
χ292-22-22-22-200002i−2i2i−2i00002-22-2-1-11-11-11i3−i3i3−i3i3−i3i3−i31−ii−ii−ii−ii−33−33−33−33002i−2i00000000000000
χ302-22-22-22-20000−2i2i−2i2i00002-22-222-22-22-200000000-2−2i2i−2i2i−2i2i−2i2i0000000000−2i2i00000000000000
χ312-22-22-22-20000−2i2i−2i2i00002-22-2-1-11-11-11−i3i3−i3i3−i3i3−i3i31i−ii−ii−ii−i−33−33−33−3300−2i2i00000000000000
χ322-22-22-22-20000−2i2i−2i2i00002-22-2-1-11-11-11i3−i3i3−i3i3−i3i3−i31i−ii−ii−ii−i3−33−33−33−300−2i2i00000000000000
χ332-2-222-2-222-22-2000000002-2-2222-2-2-2-222-2-222-2-22200000000000000002-20000000000000000
χ342-2-222-2-222-22-2000000002-2-22-1-11111-1-111-1-111-1-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i32-20000000000000000
χ352-2-222-2-222-22-2000000002-2-22-1-11111-1-111-1-111-1-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i32-20000000000000000
χ362-2-222-2-22-22-22000000002-2-2222-2-2-2-22-222-2-222-220000000000000000-220000000000000000
χ372-2-222-2-22-22-22000000002-2-22-1-11111-11-1-111-1-11-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3-220000000000000000
χ382-2-222-2-22-22-22000000002-2-22-1-11111-11-1-111-1-11-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3-220000000000000000
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
χ41333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-111111111-1-1-1-1-111-1
χ42333333333333-3-3-3-3-3-3-3-3-1-1-1-100000000000000000000000000000000-1-11111-1-1-1-111111-1-11
χ4333333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-11111-1-111-1-1-1-111
χ4433333333-3-3-3-33333-3-3-3-3-1-1-1-10000000000000000000000000000000011-1-111-1-111-1-11111-1-1
χ4533333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-111-1-1-1-111-11-11
χ4633333333-3-3-3-3-3-3-3-33333-1-1-1-1000000000000000000000000000000001111-1-1-1-11111-1-11-11-1
χ47444-4-4-4-4444-4-44i4i−4i−4i4i4i−4i−4i00001-1-1-1111-1-1-1-11111-1−i−i−i−iiiii−i−i−i−iiiii000000000000000000
χ48444-4-4-4-4444-4-4−4i−4i4i4i−4i−4i4i4i00001-1-1-1111-1-1-1-11111-1iiii−i−i−i−iiiii−i−i−i−i000000000000000000
χ49444-4-4-4-44-4-4444i4i−4i−4i−4i−4i4i4i00001-1-1-11111111-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000000000
χ50444-4-4-4-44-4-444−4i−4i4i4i4i4i−4i−4i00001-1-1-11111111-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000000000
χ5144-44-4-44-4000000004-4-4400001-1-111-1-1−i3−i3i3i3i3i3−i3−i31−i3−i3i3i3i3i3−i3−i3-1-11111-1-1000000000000000000
χ5244-44-4-44-4000000004-4-4400001-1-111-1-1i3i3−i3−i3−i3−i3i3i31i3i3−i3−i3−i3−i3i3i3-1-11111-1-1000000000000000000
χ5344-44-4-44-4000000004-4-440000-222-2-22200000000-20000000022-2-2-2-222000000000000000000
χ5444-44-4-44-400000000-444-400001-1-111-1-1−i3−i3i3i3i3i3−i3−i31i3i3−i3−i3−i3−i3i3i311-1-1-1-111000000000000000000
χ5544-44-4-44-400000000-444-400001-1-111-1-1i3i3−i3−i3−i3−i3i3i31−i3−i3i3i3i3i3−i3−i311-1-1-1-111000000000000000000
χ5644-44-4-44-400000000-444-40000-222-2-22200000000-200000000-2-22222-2-2000000000000000000
χ574-444-44-4-400004-4-44000000001-11-1-11-1−i3i3−i3i3i3−i3i3−i31-11-111-11-1−i3i3−i3i3i3−i3i3−i3000000000000000000
χ584-444-44-4-400004-4-44000000001-11-1-11-1i3−i3i3−i3−i3i3−i3i31-11-111-11-1i3−i3i3−i3−i3i3−i3i3000000000000000000
χ594-444-44-4-400004-4-4400000000-22-222-2200000000-22-22-2-22-2200000000000000000000000000
χ604-444-44-4-40000-444-4000000001-11-1-11-1−i3i3−i3i3i3−i3i3−i311-11-1-11-11i3−i3i3−i3−i3i3−i3i3000000000000000000
χ614-444-44-4-40000-444-4000000001-11-1-11-1i3−i3i3−i3−i3i3−i3i311-11-1-11-11−i3i3−i3i3i3−i3i3−i3000000000000000000
χ624-444-44-4-40000-444-400000000-22-222-2200000000-2-22-222-22-200000000000000000000000000
χ634-4-4-4-44444-4-440000000000001-111-1-11-111-11-1-11-13−3−33−333−33−3−33−333−3000000000000000000
χ644-4-4-4-44444-4-440000000000001-111-1-11-111-11-1-11-1−333−33−3−33−333−33−3−33000000000000000000
χ654-4-4-4-44444-4-44000000000000-22-2-222-22-2-22-222-220000000000000000000000000000000000
χ664-4-4-4-4444-444-40000000000001-111-1-111-1-11-111-1-13−3−33−333−3−333−33−3−33000000000000000000
χ674-4-4-4-4444-444-40000000000001-111-1-111-1-11-111-1-1−333−33−3−333−3−33−333−3000000000000000000
χ684-4-4-4-4444-444-4000000000000-22-2-222-2-222-22-2-2220000000000000000000000000000000000
χ6966-6-666-6-6000000006i−6i6i−6i-2-222000000000000000000000000000000000000−2i2i000000000000
χ7066-6-666-6-600000000−6i6i−6i6i-2-2220000000000000000000000000000000000002i−2i000000000000
χ716-66-66-66-600006i−6i6i−6i0000-22-220000000000000000000000000000000000−2i2i00000000000000
χ726-66-66-66-60000−6i6i−6i6i0000-22-2200000000000000000000000000000000002i−2i00000000000000
χ736-6-666-6-666-66-600000000-222-200000000000000000000000000000000-220000000000000000
χ746-6-666-6-66-66-6600000000-222-2000000000000000000000000000000002-20000000000000000

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