Finite Group Databasebeta

← Group #10711773

Character table — Group #10711773

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order12222344446881212666888121212242424244444161616162424484848484848484822444412121212121212124444881616161688
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
χ9111-1-111-11-1111111-1-1-1-11-1-111111ii−i−i11-1-1-1-11111-1-1-1-11-11-1i−iii−i−iii−i−iii−i−i1-111-1-1i−i
χ10111-1-111-11-1111111-1-1-1-11-1-111111ii−i−i11-1-1-1-11111-1-1-1-1-11-11i−iii−i−iii−i−i−i−iii-11-1-111−ii
χ11111-1-111-11-1111111-1-1-1-11-1-111111ii−i−i-1-111-1-1-1-1-1-111111-11-1−iiii−i−i−i−iiiii−i−i1-1-1-111−ii
χ12111-1-111-11-1111111-1-1-1-11-1-111111ii−i−i-1-111-1-1-1-1-1-11111-11-11−iiii−i−i−i−iii−i−iii-1111-1-1i−i
χ13111-1-111-11-1111111-1-1-1-11-1-111111−i−iii11-1-1-1-11111-1-1-1-11-11-1−ii−i−iii−i−iii−i−iii1-111-1-1−ii
χ14111-1-111-11-1111111-1-1-1-11-1-111111−i−iii11-1-1-1-11111-1-1-1-1-11-11−ii−i−iii−i−iiiii−i−i-11-1-111i−i
χ15111-1-111-11-1111111-1-1-1-11-1-111111−i−iii-1-111-1-1-1-1-1-111111-11-1i−i−i−iiiii−i−i−i−iii1-1-1-111i−i
χ16111-1-111-11-1111111-1-1-1-11-1-111111−i−iii-1-111-1-1-1-1-1-11111-11-11i−i−i−iiiii−i−iii−i−i-1111-1-1−ii
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
χ1922222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-2-1-1-1-11111000000000000
χ2122222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2222222-12222-122-1-1-1-1-1222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000221111-1-1-1-1000000000000
χ23222-2-222-22-22-2-2222-2-222-2-2-22-2-2-2-20000000022000000002-22-200000000000000-22000000
χ24222-2-222-22-22-2-2222-2-222-2-2-22-2-2-2-2000000002200000000-22-22000000000000002-2000000
χ25222-2-2-12-22-2-122-1-1-111-2-2211-1-1-1-1-12i2i−2i−2i22-2-211-1-1-1-1111100002i−2i−i−iii−i−iii000000000000
χ26222-2-2-12-22-2-122-1-1-111-2-2211-1-1-1-1-12i2i−2i−2i-2-222111111-1-1-1-10000−2i2i−i−iiiii−i−i000000000000
χ27222-2-2-12-22-2-122-1-1-111-2-2211-1-1-1-1-1−2i−2i2i2i22-2-211-1-1-1-111110000−2i2iii−i−iii−i−i000000000000
χ28222-2-2-12-22-2-122-1-1-111-2-2211-1-1-1-1-1−2i−2i2i2i-2-222111111-1-1-1-100002i−2iii−i−i−i−iii000000000000
χ2922-22-222-2-2220022-22-20002-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i22-2-220000000000000000−i2i2−i2i200
χ3022-22-222-2-2220022-22-20002-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2-222-20000000000000000i2−i2i2−i200
χ3122-22-222-2-2220022-22-20002-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i22-2-220000000000000000i2−i2i2−i200
χ3222-22-222-2-2220022-22-20002-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2-222-20000000000000000−i2i2−i2i200
χ3322-22-22-222-2222-2-2-22-22-2-2-22222-2-22i−2i2i−2i00002-2000000000000002i−2i2i−2i0000000000000000
χ3422-22-22-222-2222-2-2-22-22-2-2-22222-2-2−2i2i−2i2i00002-200000000000000−2i2i−2i2i0000000000000000
χ3522-22-22-222-22-2-2-2-2-22-2-222-222-2-22200000000-2200000000000000000000002i−2i2i−2i00000000
χ3622-22-22-222-22-2-2-2-2-22-2-222-222-2-22200000000-220000000000000000000000−2i2i−2i2i00000000
χ3722-22-2-1-222-2-122111-112-2-21-1-1-1-1112i−2i2i−2i0000-113−33−33−33−3000000−ii−ii−i3i3−i3i3000000000000
χ3822-22-2-1-222-2-122111-112-2-21-1-1-1-1112i−2i2i−2i0000-11−33−33−33−33000000−ii−iii3−i3i3−i3000000000000
χ3922-22-2-1-222-2-122111-112-2-21-1-1-1-111−2i2i−2i2i0000-113−33−33−33−3000000i−ii−ii3−i3i3−i3000000000000
χ4022-22-2-1-222-2-122111-112-2-21-1-1-1-111−2i2i−2i2i0000-11−33−33−33−33000000i−ii−i−i3i3−i3i3000000000000
χ4122-2-22222-2-220022-2-22000-22-200000000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i222-2-20000000000000000−i2i2i2−i200
χ4222-2-22222-2-220022-2-22000-22-200000000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i2-2-2220000000000000000i2−i2−i2i200
χ4322-2-22222-2-220022-2-22000-22-200000000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i222-2-20000000000000000i2−i2−i2i200
χ4422-2-22222-2-220022-2-22000-22-200000000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i2-2-2220000000000000000−i2i2i2−i200
χ4522-2-222-2-222222-2-2-2-22-22-22-2222-2-22-2-220000-22000000000000002-2-220000000000000000
χ4622-2-222-2-222222-2-2-2-22-22-22-2222-2-2-222-20000-2200000000000000-222-20000000000000000
χ4722-2-222-2-2222-2-2-2-2-2-222-222-22-2-222000000002-200000000000000000000002-2-2200000000
χ4822-2-222-2-2222-2-2-2-2-2-222-222-22-2-222000000002-20000000000000000000000-222-200000000
χ4922-2-22-1-2-222-1221111-1-22-2-11-1-1-1112-2-2200001-13−33−3−33−33000000-111-1−333−3000000000000
χ5022-2-22-1-2-222-1221111-1-22-2-11-1-1-1112-2-2200001-1−33−333−33−3000000-111-13−3−33000000000000
χ5122-2-22-1-2-222-1221111-1-22-2-11-1-1-111-222-200001-13−33−3−33−330000001-1-113−3−33000000000000
χ5222-2-22-1-2-222-1221111-1-22-2-11-1-1-111-222-200001-1−33−333−33−30000001-1-11−333−3000000000000
χ53444444-4-4-4-4400-4-4444000-4-4-4000000000000000000000000000000000000000000000000
χ5444444-24444-2-4-4-2-2-2-2-2-4-4-4-2-2-2222200000000220000000000000000000000000000000000
χ5544444-2-4-4-4-4-20022-2-2-200022200000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5644444-2-4-4-4-4-20022-2-2-200022200000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ57444-4-44-44-44400-4-44-4-400044-4000000000000000000000000000000000000000000000000
χ58444-4-4-24-44-4-2-4-4-2-2-22244-422-2222200000000-2-20000000000000000000000000000000000
χ59444-4-4-2-44-44-20022-222000-2-2200000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ60444-4-4-2-44-44-20022-222000-2-2200000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6144-44-4-24-4-44-200-2-22-22000-22200000000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ6244-44-4-24-4-44-200-2-22-22000-222000000002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ6344-44-4-2-444-4-2-4-4222-22-4442-2-222-2-2000000002-20000000000000000000000000000000000
χ6444-4-44-244-4-4-200-2-222-20002-2200000000−2i22i22i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ6544-4-44-244-4-4-200-2-222-20002-22000000002i2−2i2−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ6644-4-44-2-4-444-2-4-42222-24-44-22-222-2-200000000-220000000000000000000000000000000000
χ678-800080000-8−4i24i200000000000−4i24i20000000000000000000000000000000000000000000000
χ688-800080000-84i2−4i2000000000004i2−4i20000000000000000000000000000000000000000000000
χ698-8000-400004−4i24i243−430000000002i2−2i22i6−2i600000000000000000000000000000000000000000000
χ708-8000-400004−4i24i2−43430000000002i2−2i2−2i62i600000000000000000000000000000000000000000000
χ718-8000-4000044i2−4i243−43000000000−2i22i2−2i62i600000000000000000000000000000000000000000000
χ728-8000-4000044i2−4i2−4343000000000−2i22i22i6−2i600000000000000000000000000000000000000000000

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