Finite Group Databasebeta

← Group #10691186

Character table — Group #10691186

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order122222344446666666444444441212121244121212121212121212121212444412121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-111-1-111-1-1-1-1111-1-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-111-1-111-1-1-1-1111-1-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-111-1-111-1-1-1-111-111-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-111-1-111-1-1-1-111-111-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-22222-2-22222-2-2-2-222-2-2-2-2-2-2220000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-222-2-222-2-20000000000000000000000000000
χ192222222-2-2-2-22222222-2-222-2-222-2-2-2-22-2-2-2222222-2-2-2-20000000000000000000000000000
χ202222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-22-2-2-2-2-2-22222220000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-2-1-11111-1-1111122-2-21111-1-1-1-10000000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-2-1-11111-1-11111-2-222-1-1-1-111110000000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-211-1-1111111-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-211-1-1111111-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1221111-1-111-1-1110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1221111-1-111-1-1110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-22-1-1-1-11111-1-1112-22-2-1-111-1-1110000000000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-22-1-1-1-11111-1-111-22-2211-1-111-1-10000000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211112-2-1-111-1-11111-1-12-2-2211-1-1-1-1110000000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211112-2-1-111-1-11111-1-1-222-2-1-11111-1-10000000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211112-211-1-1-1-1-1-111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211112-211-1-1-1-1-1-111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ35222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-22111111-1-1-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ36222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-22111111-1-1-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ372222-2-2222-2-2-2-2-2-22222-200002-222-2-2002-200002-2000000000000000000002i−2i2i−2i00000000
χ382222-2-2222-2-2-2-2-2-22222-200002-222-2-2002-200002-200000000000000000000−2i2i−2i2i00000000
χ392222-2-2222-2-2-2-2-2-2222-220000-2222-2-200-220000-2200000000000000002i−2i2i−2i000000000000
χ402222-2-2222-2-2-2-2-2-2222-220000-2222-2-200-220000-220000000000000000−2i2i−2i2i000000000000
χ412222-2-22-2-222-2-2-2-22222-20000-22-2-222002-20000-22000000000000000000002-2-2200000000
χ422222-2-22-2-222-2-2-2-22222-20000-22-2-222002-20000-2200000000000000000000-222-200000000
χ432222-2-22-2-222-2-2-2-2222-2200002-2-2-22200-2200002-200000000000000002-2-22000000000000
χ442222-2-22-2-222-2-2-2-2222-2200002-2-2-22200-2200002-20000000000000000-222-2000000000000
χ452-2-222-222i−2i2i−2i22-2-2-2-22002i−2i2-2002i−2i2i−2i00002i−2i0000002-2000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ462-2-222-222i−2i2i−2i22-2-2-2-22002i−2i2-2002i−2i2i−2i00002i−2i0000002-200000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ472-2-222-222i−2i2i−2i22-2-2-2-2200−2i2i-22002i−2i2i−2i0000−2i2i000000-22000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ482-2-222-222i−2i2i−2i22-2-2-2-2200−2i2i-22002i−2i2i−2i0000−2i2i000000-2200000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ492-2-222-22−2i2i−2i2i22-2-2-2-22002i−2i-2200−2i2i−2i2i00002i−2i000000-22000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ502-2-222-22−2i2i−2i2i22-2-2-2-22002i−2i-2200−2i2i−2i2i00002i−2i000000-2200000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ512-2-222-22−2i2i−2i2i22-2-2-2-2200−2i2i2-200−2i2i−2i2i0000−2i2i0000002-2000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ522-2-222-22−2i2i−2i2i22-2-2-2-2200−2i2i2-200−2i2i−2i2i0000−2i2i0000002-200000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ534444-4-4-244-4-42222-2-2-24-400004-4-2-22200-220000-2200000000000000000000000000000000
χ544444-4-4-244-4-42222-2-2-2-440000-44-2-222002-200002-200000000000000000000000000000000
χ554444-4-4-2-4-4442222-2-2-24-40000-4422-2-200-2200002-200000000000000000000000000000000
χ564444-4-4-2-4-4442222-2-2-2-4400004-422-2-2002-20000-2200000000000000000000000000000000
χ574-4-444-4-24i−4i4i−4i-2-22222-2004i−4i4-400−2i2i−2i2i0000−2i2i000000-220000000000000000000000000000
χ584-4-444-4-24i−4i4i−4i-2-22222-200−4i4i-4400−2i2i−2i2i00002i−2i0000002-20000000000000000000000000000
χ594-4-444-4-2−4i4i−4i4i-2-22222-2004i−4i-44002i−2i2i−2i0000−2i2i0000002-20000000000000000000000000000
χ604-4-444-4-2−4i4i−4i4i-2-22222-200−4i4i4-4002i−2i2i−2i00002i−2i000000-220000000000000000000000000000
χ614-4-44-4444i−4i−4i4i-4-444-4-44000000004i−4i−4i4i000000000000000000000000000000000000000000
χ624-4-44-444−4i4i4i−4i-4-444-4-4400000000−4i4i4i−4i000000000000000000000000000000000000000000
χ634-4-44-44-24i−4i−4i4i22-2-222-200000000−2i2i2i−2i00000023−2300−2i32i3000000000000000000000000000000
χ644-4-44-44-24i−4i−4i4i22-2-222-200000000−2i2i2i−2i000000−2323002i3−2i3000000000000000000000000000000
χ654-4-44-44-2−4i4i4i−4i22-2-222-2000000002i−2i−2i2i00000023−23002i3−2i3000000000000000000000000000000
χ664-4-44-44-2−4i4i4i−4i22-2-222-2000000002i−2i−2i2i000000−232300−2i32i3000000000000000000000000000000
χ6788-8-8008000000008-8-8000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000−4i34i3−4i34i3-444000000000000000000000000000000000000000000000000000000
χ6988-8-800-400004i3−4i34i3−4i3-444000000000000000000000000000000000000000000000000000000
χ708-88-800800000000-88-8000000000000000000000000000000000000000000000000000000
χ718-88-800-40000−4i34i34i3−4i34-44000000000000000000000000000000000000000000000000000000
χ728-88-800-400004i3−4i3−4i34i34-44000000000000000000000000000000000000000000000000000000

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