Finite Group Databasebeta

← Group #10712413

Character table — Group #10712413

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222344446881212666888121212242424248888161616162424484848484848484888888824242424242424242244441616161622
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-1-1
χ9111-1-1111-1-1111111-1-11-1-11-1-11111ii−i−i11-1-1-1-11111-1-1-1-1ii−i−ii−iii−i−iii−i−i11-1-1i−iii−i−i1-1
χ10111-1-1111-1-1111111-1-11-1-11-1-11111ii−i−i11-1-1-1-11111-1-1-1-1−i−iiii−iii−i−iii−i−i-1-111−ii−i−iii-11
χ11111-1-1111-1-1111111-1-11-1-11-1-11111ii−i−i-1-111-1-1-1-1-1-11111ii−i−i−iiii−i−i−i−iii11-1-1i−i−i−iii-11
χ12111-1-1111-1-1111111-1-11-1-11-1-11111ii−i−i-1-111-1-1-1-1-1-11111−i−iii−iiii−i−i−i−iii-1-111−iiii−i−i1-1
χ13111-1-1111-1-1111111-1-11-1-11-1-11111−i−iii11-1-1-1-11111-1-1-1-1ii−i−i−ii−i−iii−i−iii-1-111i−iii−i−i-11
χ14111-1-1111-1-1111111-1-11-1-11-1-11111−i−iii11-1-1-1-11111-1-1-1-1−i−iii−ii−i−iii−i−iii11-1-1−ii−i−iii1-1
χ15111-1-1111-1-1111111-1-11-1-11-1-11111−i−iii-1-111-1-1-1-1-1-11111ii−i−ii−i−i−iiiii−i−i-1-111i−i−i−iii1-1
χ16111-1-1111-1-1111111-1-11-1-11-1-11111−i−iii-1-111-1-1-1-1-1-11111−i−iiii−i−i−iiiii−i−i11-1-1−iiii−i−i-11
χ1722222222222-2-222222-2-2-2222-2-2-2-200000000-2-200000000222200000000000000-2-2000000
χ1822222222222-2-222222-2-2-2222-2-2-2-200000000-2-200000000-2-2-2-20000000000000022000000
χ19222222-2-2-2-2200-2-2222000-2-2-2000000002−22−20022−2−222−2−22i−2i2i−2i0000000000000000−i2i2−i2i200
χ20222222-2-2-2-2200-2-2222000-2-2-2000000002−22−20022−2−222−2−2−2i2i−2i2i0000000000000000i2−i2i2−i200
χ21222222-2-2-2-2200-2-2222000-2-2-200000000−22−2200−2−222−2−2222i−2i2i−2i0000000000000000i2−i2i2−i200
χ22222222-2-2-2-2200-2-2222000-2-2-200000000−22−2200−2−222−2−222−2i2i−2i2i0000000000000000−i2i2−i2i200
χ2322222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2422222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ2522222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2622222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ27222-2-2222-2-22-2-2222-2-2-2222-2-2-2-2-2-20000000022000000002i2i−2i−2i00000000000000−2i2i000000
χ28222-2-2222-2-22-2-2222-2-2-2222-2-2-2-2-2-2000000002200000000−2i−2i2i2i000000000000002i−2i000000
χ29222-2-22-2-222200-2-22-2-2000-222000000002−2−220022−2−2−2−2222-2-220000000000000000−222−200
χ30222-2-22-2-222200-2-22-2-2000-222000000002−2−220022−2−2−2−222-222-200000000000000002−2−2200
χ31222-2-22-2-222200-2-22-2-2000-22200000000−222−200−2−22222−2−22-2-2200000000000000002−2−2200
χ32222-2-22-2-222200-2-22-2-2000-22200000000−222−200−2−22222−2−2-222-20000000000000000−222−200
χ33222-2-2-122-2-2-122-1-1-1112-2-2-111-1-1-1-12i2i−2i−2i22-2-211-1-1-1-1111100002i−2i−i−iii−i−iii000000000000
χ34222-2-2-122-2-2-122-1-1-1112-2-2-111-1-1-1-12i2i−2i−2i-2-222111111-1-1-1-10000−2i2i−i−iiiii−i−i000000000000
χ35222-2-2-122-2-2-122-1-1-1112-2-2-111-1-1-1-1−2i−2i2i2i22-2-211-1-1-1-111110000−2i2iii−i−iii−i−i000000000000
χ36222-2-2-122-2-2-122-1-1-1112-2-2-111-1-1-1-1−2i−2i2i2i-2-222111111-1-1-1-100002i−2iii−i−i−i−iii000000000000
χ3722-22-22-222-2222-2-2-22-2-2-2222-2-2-222000000002-200000000000000000000002-22-200000000
χ3822-22-22-222-2222-2-2-22-2-2-2222-2-2-222000000002-20000000000000000000000-22-2200000000
χ3922-22-22-222-22-2-2-2-2-22-222-222-222-2-22i−2i2i−2i0000-22000000000000002i−2i2i−2i0000000000000000
χ4022-22-22-222-22-2-2-2-2-22-222-222-222-2-2−2i2i−2i2i0000-2200000000000000−2i2i−2i2i0000000000000000
χ4122-22-2-1-222-2-1-2-2111-1122-2-1-11-1-1112i−2i2i−2i00001-13−33−33−33−3000000−ii−ii−i3i3−i3i3000000000000
χ4222-22-2-1-222-2-1-2-2111-1122-2-1-11-1-1112i−2i2i−2i00001-1−33−33−33−33000000−ii−iii3−i3i3−i3000000000000
χ4322-22-2-1-222-2-1-2-2111-1122-2-1-11-1-111−2i2i−2i2i00001-13−33−33−33−3000000i−ii−ii3−i3i3−i3000000000000
χ4422-22-2-1-222-2-1-2-2111-1122-2-1-11-1-111−2i2i−2i2i00001-1−33−33−33−33000000i−ii−i−i3i3−i3i3000000000000
χ4522-2-222-22-22222-2-2-2-22-22-22-22-2-22200000000-2200000000000000000000002-2-2200000000
χ4622-2-222-22-22222-2-2-2-22-22-22-22-2-22200000000-220000000000000000000000-222-200000000
χ4722-2-222-22-222-2-2-2-2-2-222-222-2222-2-22-2-2200002-2000000000000002-2-220000000000000000
χ4822-2-222-22-222-2-2-2-2-2-222-222-2222-2-2-222-200002-200000000000000-222-20000000000000000
χ4922-2-22-1-22-22-1-2-21111-12-22-11-1-1-1112-2-220000-113−33−3−33−33000000-111-1−333−3000000000000
χ5022-2-22-1-22-22-1-2-21111-12-22-11-1-1-1112-2-220000-11−33−333−33−3000000-111-13−3−33000000000000
χ5122-2-22-1-22-22-1-2-21111-12-22-11-1-1-111-222-20000-113−33−3−33−330000001-1-113−3−33000000000000
χ5222-2-22-1-22-22-1-2-21111-12-22-11-1-1-111-222-20000-11−33−333−33−30000001-1-11−333−3000000000000
χ5344444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200000000220000000000000000000000000000000000
χ5444444-2-4-4-4-4-20022-2-2-20002220000000022−2222−2200−2−222−2−22200000000000000000000000000
χ5544444-2-4-4-4-4-20022-2-2-200022200000000−2222−22220022−2−222−2−200000000000000000000000000
χ56444-4-4-244-4-4-2-4-4-2-2-222-444-222222200000000-2-20000000000000000000000000000000000
χ57444-4-4-2-4-444-20022-2220002-2-20000000022−22−222200−2−22222−2−200000000000000000000000000
χ58444-4-4-2-4-444-20022-2220002-2-200000000−222222−220022−2−2−2−22200000000000000000000000000
χ5944-44-444-4-4440044-44-4000-4-44000000000000000000000000000000000000000000000000
χ6044-44-4-24-4-44-200-2-22-2200022-2000000000000006−6−666−6−6600000000000000000000000000
χ6144-44-4-24-4-44-200-2-22-2200022-200000000000000−666−6−666−600000000000000000000000000
χ6244-44-4-2-444-4-244222-22-4-44-2-2222-2-200000000-220000000000000000000000000000000000
χ6344-4-4444-44-440044-4-44000-44-4000000000000000000000000000000000000000000000000
χ6444-4-44-24-44-4-200-2-222-20002-22000000000000006−6−66−666−600000000000000000000000000
χ6544-4-44-24-44-4-200-2-222-20002-2200000000000000−666−66−6−6600000000000000000000000000
χ6644-4-44-2-44-44-2442222-2-44-4-22-222-2-2000000002-20000000000000000000000000000000000
χ678-800080000-842−42000000000000042−4200000000000000000000000000000000000000000000
χ688-800080000-8−42420000000000000−424200000000000000000000000000000000000000000000
χ698-8000-40000442−4243−4300000000026−26−222200000000000000000000000000000000000000000000
χ708-8000-40000442−42−4343000000000−2626−222200000000000000000000000000000000000000000000
χ718-8000-400004−424243−43000000000−262622−2200000000000000000000000000000000000000000000
χ728-8000-400004−4242−434300000000026−2622−2200000000000000000000000000000000000000000000

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