Finite Group Databasebeta

← Group #10710928

Character table — Group #10710928

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order122223444466688668881212121224242424222216161616242448484848484848482244666688242424242244881616161644
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ9111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-111-1-1ii−i−i11iiii−i−i−i−i1-11-111-1-1i−iii−i−i1-11-11-1ii−i−ii−i
χ10111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-111-1-1ii−i−i11iiii−i−i−i−i-11-1111-1-1i−iii−i−i-11-11-11−i−iii−ii
χ11111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-111-1-1−i−iii11−i−i−i−iiiii1-11-111-1-1−ii−i−iii1-11-11-1−i−iii−ii
χ12111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-111-1-1−i−iii11−i−i−i−iiiii-11-1111-1-1−ii−i−iii-11-11-11ii−i−ii−i
χ13111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-1-1-111ii−i−i11iiii−i−i−i−i1-11-1-1-111−ii−i−iii-11-111-1ii−i−i−ii
χ14111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-1-1-111ii−i−i11iiii−i−i−i−i-11-11-1-111−ii−i−iii1-11-1-11−i−iiii−i
χ15111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-1-1-111−i−iii11−i−i−i−iiiii1-11-1-1-111i−iii−i−i-11-111-1−i−iiii−i
χ16111-1-111-1-11111-1-1-1-111-11-11-1-1-1-1-1-1-111−i−iii11−i−i−i−iiiii-11-11-1-111i−iii−i−i1-11-1-11ii−i−i−ii
χ172222222222222-2-222-2-2-22222-2-2-2-200000000-2-200000000222200000000000000-2-2000000
χ182222222222222-2-222-2-2-22222-2-2-2-200000000-2-200000000-2-2-2-20000000000000022000000
χ1922222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-1-1-122-1-1-1-1000000000000
χ2022222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-1-1-1-1-2-21111000000000000
χ2122222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100001111-2-21111000000000000
χ2222222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000111122-1-1-1-1000000000000
χ23222-2-222-2-2222222-2-2-2-222-22-2222200000000-2-2000000002-22-200000000000000-22000000
χ24222-2-222-2-2222222-2-2-2-222-22-2222200000000-2-200000000-22-22000000000000002-2000000
χ25222-2-2-12-2-22-1-1-1-2-21122-2-11-11111122-2-22i2i−2i−2i-1-1−i−i−i−iiiii0000-1-1112i−2i−i−iii000000000000
χ26222-2-2-12-2-22-1-1-1-2-21122-2-11-11111122-2-2−2i−2i2i2i-1-1iiii−i−i−i−i0000-1-111−2i2iii−i−i000000000000
χ27222-2-2-12-2-22-1-1-1-2-21122-2-11-111111-2-2222i2i−2i−2i-1-1−i−i−i−iiiii000011-1-1−2i2iii−i−i000000000000
χ28222-2-2-12-2-22-1-1-1-2-21122-2-11-111111-2-222−2i−2i2i2i-1-1iiii−i−i−i−i000011-1-12i−2i−i−iii000000000000
χ2922-22-2222-2-2-2-22002-200022-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i222-2-20000000000000000−i2i2−i2i200
χ3022-22-2222-2-2-2-22002-200022-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2-2-2220000000000000000i2−i2i2−i200
χ3122-22-2222-2-2-2-22002-200022-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i222-2-20000000000000000i2−i2i2−i200
χ3222-22-2222-2-2-2-22002-200022-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2-2-2220000000000000000−i2i2−i2i200
χ3322-22-22-2-222-2-22222-22-2-2-2-22222-2-2000000002-2000000000000000000000022-2-200000000
χ3422-22-22-2-222-2-22222-22-2-2-2-22222-2-2000000002-20000000000000000000000-2-22200000000
χ3522-22-22-2-222-2-22-2-22-2-222-2-222-2-2222-22-20000-220000000000002-22-2000000000000000000
χ3622-22-22-2-222-2-22-2-22-2-222-2-222-2-222-22-220000-22000000000000-22-22000000000000000000
χ3722-22-2-1-2-22211-1-2-2-11-22211-1-111-1-12-22-200001-1−i3i3−i3i3−i3i3−i3i30000-11-1100−i3i3−i3i3000000000000
χ3822-22-2-1-2-22211-1-2-2-11-22211-1-111-1-12-22-200001-1i3−i3i3−i3i3−i3i3−i30000-11-1100i3−i3i3−i3000000000000
χ3922-22-2-1-2-22211-1-2-2-11-22211-1-111-1-1-22-2200001-1−i3i3−i3i3−i3i3−i3i300001-11-100i3−i3i3−i3000000000000
χ4022-22-2-1-2-22211-1-2-2-11-22211-1-111-1-1-22-2200001-1i3−i3i3−i3i3−i3i3−i300001-11-100−i3i3−i3i3000000000000
χ4122-2-2222-22-2-2-2200-220002-2-22000000002−2−220022−2−2−2−2222-2-2200000000000000002−2−2200
χ4222-2-2222-22-2-2-2200-220002-2-22000000002−2−220022−2−2−2−222-222-20000000000000000−222−200
χ4322-2-2222-22-2-2-2200-220002-2-2200000000−222−200−2−22222−2−22-2-220000000000000000−222−200
χ4422-2-2222-22-2-2-2200-220002-2-2200000000−222−200−2−22222−2−2-222-200000000000000002−2−2200
χ4522-2-222-22-22-2-2222-22-22-2-222-222-2-22-2-220000-220000000000002-2-22000000000000000000
χ4622-2-222-22-22-2-2222-22-22-2-222-222-2-2-222-20000-22000000000000-222-2000000000000000000
χ4722-2-222-22-22-2-22-2-2-222-22-222-2-2-222000000002-200000000000000000000002-2-2200000000
χ4822-2-222-22-22-2-22-2-2-222-22-222-2-2-222000000002-20000000000000000000000-222-200000000
χ4922-2-22-1-22-2211-1221-1-22-21-1-11-1-1112-2-2200001-13−33−3−33−330000-111-1003−3−33000000000000
χ5022-2-22-1-22-2211-1221-1-22-21-1-11-1-1112-2-2200001-1−33−333−33−30000-111-100−333−3000000000000
χ5122-2-22-1-22-2211-1221-1-22-21-1-11-1-111-222-200001-13−33−3−33−3300001-1-1100−333−3000000000000
χ5222-2-22-1-22-2211-1221-1-22-21-1-11-1-111-222-200001-1−33−333−33−300001-1-11003−3−33000000000000
χ53444444-4-4-4-44440044000-4-4-4-4000000000000000000000000000000000000000000000000
χ5444444-24444-2-2-2-4-4-2-2-4-4-4-2-2-2-2222200000000220000000000000000000000000000000000
χ5544444-2-4-4-4-4-2-2-200-2-20002222000000000000006−6−666−6−6600000000000000000000000000
χ5644444-2-4-4-4-4-2-2-200-2-2000222200000000000000−666−6−666−600000000000000000000000000
χ57444-4-44-444-444400-4-4000-44-44000000000000000000000000000000000000000000000000
χ58444-4-4-24-4-44-2-2-24422-4-44-22-22-2-2-2-200000000220000000000000000000000000000000000
χ59444-4-4-2-444-4-2-2-200220002-22-200000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ60444-4-4-2-444-4-2-2-200220002-22-200000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6144-44-4-244-4-422-200-22000-2-22200000000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ6244-44-4-244-4-422-200-22000-2-222000000002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ6344-44-4-2-4-44422-244-224-4-422-2-2-2-22200000000-220000000000000000000000000000000000
χ6444-4-44-24-44-422-2002-2000-222-20000000022−22−222200−2−22222−2−200000000000000000000000000
χ6544-4-44-24-44-422-2002-2000-222-200000000−222222−220022−2−2−2−22200000000000000000000000000
χ6644-4-44-2-44-4422-2-4-42-24-442-2-2222-2-200000000-220000000000000000000000000000000000
χ678-80008000000-842−4200000000042−420000000000000000000000000000000000000000000000
χ688-80008000000-8−4242000000000−42420000000000000000000000000000000000000000000000
χ698-8000-40000−4i34i3442−42000000000−22222i6−2i600000000000000000000000000000000000000000000
χ708-8000-40000−4i34i34−424200000000022−22−2i62i600000000000000000000000000000000000000000000
χ718-8000-400004i3−4i3442−42000000000−2222−2i62i600000000000000000000000000000000000000000000
χ728-8000-400004i3−4i34−424200000000022−222i6−2i600000000000000000000000000000000000000000000

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