Finite Group Databasebeta

← Group #10711775

Character table — Group #10711775

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11222222222222244444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222234444666886688812121212242424244444161616162424484848484848484822444412121212121212124444881616161688
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
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
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1
χ9111-1-111-11-11-1-1111-1-1-111-1-11-1-111ii−i−i11-1-11-11111-1-1-1-11-11-1i−iii−i−iii−i−iii−i−i1-111-1-1i−i
χ10111-1-111-11-11-1-1111-1-1-111-1-11-1-111ii−i−i11-1-11-11111-1-1-1-1-11-11i−iii−i−iii−i−i−i−iii-11-1-111−ii
χ11111-1-111-11-11-1-1111-1-1-111-1-11-1-111ii−i−i-1-1111-1-1-1-1-111111-11-1−ii−i−iiiii−i−iii−i−i1-1-1-111−ii
χ12111-1-111-11-11-1-1111-1-1-111-1-11-1-111ii−i−i-1-1111-1-1-1-1-11111-11-11−ii−i−iiiii−i−i−i−iii-1111-1-1i−i
χ13111-1-111-11-11-1-1111-1-1-111-1-11-1-111−i−iii11-1-11-11111-1-1-1-11-11-1−ii−i−iii−i−iii−i−iii1-111-1-1−ii
χ14111-1-111-11-11-1-1111-1-1-111-1-11-1-111−i−iii11-1-11-11111-1-1-1-1-11-11−ii−i−iii−i−iiiii−i−i-11-1-111i−i
χ15111-1-111-11-11-1-1111-1-1-111-1-11-1-111−i−iii-1-1111-1-1-1-1-111111-11-1i−iii−i−i−i−iii−i−iii1-1-1-111i−i
χ16111-1-111-11-11-1-1111-1-1-111-1-11-1-111−i−iii-1-1111-1-1-1-1-11111-11-11i−iii−i−i−i−iiiii−i−i-1111-1-1−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
χ1922222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-21111-1-1-1-1000000000000
χ2122222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ2222222-12222-1-1-122-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000022-1-1-1-11111000000000000
χ23222-2-222-22-22-2-2-2-22-222-22-2-2222-2-200000000-22000000002-22-200000000000000-22000000
χ24222-2-222-22-22-2-2-2-22-222-22-2-2222-2-200000000-2200000000-22-22000000000000002-2000000
χ25222-2-2-12-22-2-11122-11-2-22-111-111-1-12i2i−2i−2i22-2-2-11-1-1-1-1111100002i−2i−i−iii−i−iii000000000000
χ26222-2-2-12-22-2-11122-11-2-22-111-111-1-12i2i−2i−2i-2-222-111111-1-1-1-10000−2i2iii−i−i−i−iii000000000000
χ27222-2-2-12-22-2-11122-11-2-22-111-111-1-1−2i−2i2i2i22-2-2-11-1-1-1-111110000−2i2iii−i−iii−i−i000000000000
χ28222-2-2-12-22-2-11122-11-2-22-111-111-1-1−2i−2i2i2i-2-222-111111-1-1-1-100002i−2i−i−iiiii−i−i000000000000
χ2922-22-222-2-2222200-2-200022-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i22-2-220000000000000000−i2i2−i2i200
χ3022-22-222-2-2222200-2-200022-2-200000000−i2i2−i2i200−i2−i2i2i2−i2−i2i2i2-222-20000000000000000i2−i2i2−i200
χ3122-22-222-2-2222200-2-200022-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i22-2-220000000000000000i2−i2i2−i200
χ3222-22-222-2-2222200-2-200022-2-200000000i2−i2i2−i200i2i2−i2−i2i2i2−i2−i2-222-20000000000000000−i2i2−i2i200
χ3322-22-22-222-222222-2-22-2-2-2-222222200000000-2-200000000000000000000002i−2i2i−2i00000000
χ3422-22-22-222-222222-2-22-2-2-2-222222200000000-2-20000000000000000000000−2i2i−2i2i00000000
χ3522-22-22-222-2222-2-2-2-2-222-2-222-2-2-2-22i−2i2i−2i0000220000000000000000002i−2i2i−2i000000000000
χ3622-22-22-222-2222-2-2-2-2-222-2-222-2-2-2-2−2i2i−2i2i000022000000000000000000−2i2i−2i2i000000000000
χ3722-22-2-1-222-2-1-1-1-2-211-22211-1-111112i−2i2i−2i0000-1-13−33−33−33−3000000−i3i3−i3i3−ii−ii000000000000
χ3822-22-2-1-222-2-1-1-1-2-211-22211-1-111112i−2i2i−2i0000-1-1−33−33−33−33000000i3−i3i3−i3−ii−ii000000000000
χ3922-22-2-1-222-2-1-1-1-2-211-22211-1-11111−2i2i−2i2i0000-1-13−33−33−33−3000000i3−i3i3−i3i−ii−i000000000000
χ4022-22-2-1-222-2-1-1-1-2-211-22211-1-11111−2i2i−2i2i0000-1-1−33−33−33−33000000−i3i3−i3i3i−ii−i000000000000
χ4122-2-22222-2-22-2-200-220002-22-200000000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i222-2-20000000000000000−i2i2i2−i200
χ4222-2-22222-2-22-2-200-220002-22-200000000−i2i2i2−i200−i2−i2i2i2i2i2−i2−i2-2-2220000000000000000i2−i2−i2i200
χ4322-2-22222-2-22-2-200-220002-22-200000000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i222-2-20000000000000000i2−i2−i2i200
χ4422-2-22222-2-22-2-200-220002-22-200000000i2−i2−i2i200i2i2−i2−i2−i2−i2i2i2-2-2220000000000000000−i2i2i2−i200
χ4522-2-222-2-2222-2-222-22-22-2-22-22-2-22200000000-2200000000000000000000002-2-2200000000
χ4622-2-222-2-2222-2-222-22-22-2-22-22-2-22200000000-220000000000000000000000-222-200000000
χ4722-2-222-2-2222-2-2-2-2-222-22-22-2222-2-22-2-2200002-20000000000000000002-2-22000000000000
χ4822-2-222-2-2222-2-2-2-2-222-22-22-2222-2-2-222-200002-2000000000000000000-222-2000000000000
χ4922-2-22-1-2-222-111-2-21-12-221-11-1-1-1112-2-220000-113−33−3−33−33000000−333−3-111-1000000000000
χ5022-2-22-1-2-222-111-2-21-12-221-11-1-1-1112-2-220000-11−33−333−33−30000003−3−33-111-1000000000000
χ5122-2-22-1-2-222-111-2-21-12-221-11-1-1-111-222-20000-113−33−3−33−330000003−3−331-1-11000000000000
χ5222-2-22-1-2-222-111-2-21-12-221-11-1-1-111-222-20000-11−33−333−33−3000000−333−31-1-11000000000000
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
χ5544444-2-4-4-4-4-2-2-200-2-2000222200000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5644444-2-4-4-4-4-2-2-200-2-2000222200000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ57444-4-44-44-444-4-4004-4000-444-4000000000000000000000000000000000000000000000000
χ58444-4-4-24-44-4-222-4-4-2244-4-222-2-2-222000000002-20000000000000000000000000000000000
χ59444-4-4-2-44-44-22200-220002-2-2200000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ60444-4-4-2-44-44-22200-220002-2-2200000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ6144-44-4-24-4-44-2-2-20022000-2-22200000000−2i22i2−2i22i200i2i2−i2−i2i2i2−i2−i200000000000000000000000000
χ6244-44-4-24-4-44-2-2-20022000-2-222000000002i2−2i22i2−2i200−i2−i2i2i2−i2−i2i2i200000000000000000000000000
χ6344-44-4-2-444-4-2-2-244224-4-422-2-2-2-2-2-200000000220000000000000000000000000000000000
χ6444-4-44-244-4-4-222002-2000-22-2200000000−2i22i22i2−2i200i2i2−i2−i2−i2−i2i2i200000000000000000000000000
χ6544-4-44-244-4-4-222002-2000-22-22000000002i2−2i2−2i22i200−i2−i2i2i2i2i2−i2−i200000000000000000000000000
χ6644-4-44-2-4-444-222442-2-44-42-22-222-2-2000000002-20000000000000000000000000000000000
χ678-800080000-800−4i24i200000000000−4i24i200000000000000000000000000000000000000000000
χ688-800080000-8004i2−4i2000000000004i2−4i200000000000000000000000000000000000000000000
χ698-8000-400004−4i34i3−4i24i200000000026−262i2−2i200000000000000000000000000000000000000000000
χ708-8000-400004−4i34i34i2−4i2000000000−2626−2i22i200000000000000000000000000000000000000000000
χ718-8000-4000044i3−4i3−4i24i2000000000−26262i2−2i200000000000000000000000000000000000000000000
χ728-8000-4000044i3−4i34i2−4i200000000026−26−2i22i200000000000000000000000000000000000000000000

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