Finite Group Databasebeta

← Group #10691206

Character table — Group #10691206

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order1222223444466666664444444412121212246612121212121212121212444412121212121212128888888888888888
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
χ511111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-11111-1-1-1-1-1-1111-1-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-11111-1-1-1-1-1-1111-1-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-11111-1-1-1-1-1-111-111-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-1111111111-1-111-1-1-1-1-1-11-11111-1-1-1-1-1-111-111-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-22222-2-22222-2-2-2-2-2-222-2-2-2-2220000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-20000000000000000000000000000
χ192222222-2-2-2-22222222-2-222-2-222-2-2-2-22-222-2-222-2-222-2-20000000000000000000000000000
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
χ23222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-211-1-11111-1-11122-2-21111-1-1-1-10000000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-211-1-11111-1-111-2-222-1-1-1-111110000000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-21111-1-11111-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-21111-1-11111-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-11111-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-11111-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-2211-1-1-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-2211-1-1-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211112-2-1-1-1-1111111-1-12-2-2211-1-1-1-1110000000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211112-2-1-1-1-1111111-1-1-222-2-1-11111-1-10000000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211112-2-1-111-1-111-1-1110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211112-2-1-111-1-111-1-1110000i3−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
χ372222-2-2222-2-2-2-222-2-222-200002-222-2-200002-200002-20000000000000000002i−2i2i−2i00000000
χ382222-2-2222-2-2-2-222-2-222-200002-222-2-200002-200002-2000000000000000000−2i2i−2i2i00000000
χ392222-2-2222-2-2-2-222-2-22-220000-2222-2-20000-220000-22000000000000002i−2i2i−2i000000000000
χ402222-2-2222-2-2-2-222-2-22-220000-2222-2-20000-220000-2200000000000000−2i2i−2i2i000000000000
χ412222-2-22-2-222-2-222-2-222-20000-22-2-22200002-20000-220000000000000000002-2-2200000000
χ422222-2-22-2-222-2-222-2-222-20000-22-2-22200002-20000-22000000000000000000-222-200000000
χ432222-2-22-2-222-2-222-2-22-2200002-2-2-2220000-2200002-2000000000000002-2-22000000000000
χ442222-2-22-2-222-2-222-2-22-2200002-2-2-2220000-2200002-200000000000000-222-2000000000000
χ4522-2-2-2222-22-2-2-22-222-2002i−2i2i−2i002-22-20000002i−2i00002i−2i00000000000000000000−i2i2−i2i22−22−2
χ4622-2-2-2222-22-2-2-22-222-2002i−2i2i−2i002-22-20000002i−2i00002i−2i00000000000000000000i2−i2i2−i2−22−22
χ4722-2-2-2222-22-2-2-22-222-200−2i2i−2i2i002-22-2000000−2i2i0000−2i2i00000000000000000000−i2i2−i2i2−22−22
χ4822-2-2-2222-22-2-2-22-222-200−2i2i−2i2i002-22-2000000−2i2i0000−2i2i00000000000000000000i2−i2i2−i22−22−2
χ4922-2-2-222-22-22-2-22-222-2002i−2i−2i2i00-22-220000002i−2i0000−2i2i000000000000000000002−2−22i2−i2−i2i2
χ5022-2-2-222-22-22-2-22-222-2002i−2i−2i2i00-22-220000002i−2i0000−2i2i00000000000000000000−222−2−i2i2i2−i2
χ5122-2-2-222-22-22-2-22-222-200−2i2i2i−2i00-22-22000000−2i2i00002i−2i000000000000000000002−2−22−i2i2i2−i2
χ5222-2-2-222-22-22-2-22-222-200−2i2i2i−2i00-22-22000000−2i2i00002i−2i00000000000000000000−222−2i2−i2−i2i2
χ534444-4-4-244-4-422-2-222-24-400004-4-2-2220000-220000-22000000000000000000000000000000
χ544444-4-4-244-4-422-2-222-2-440000-44-2-22200002-200002-2000000000000000000000000000000
χ554444-4-4-2-4-44422-2-222-24-40000-4422-2-20000-2200002-2000000000000000000000000000000
χ564444-4-4-2-4-44422-2-222-2-4400004-422-2-200002-20000-22000000000000000000000000000000
χ5744-4-44-444-4-44444-4-4-4-4000000004-4-44000000000000000000000000000000000000000000
χ5844-4-44-44-444-4444-4-4-4-400000000-444-4000000000000000000000000000000000000000000
χ5944-4-44-4-24-4-44-2-2-2222200000000-222-200−2i32i30000−2i32i300000000000000000000000000000000
χ6044-4-44-4-24-4-44-2-2-2222200000000-222-2002i3−2i300002i3−2i300000000000000000000000000000000
χ6144-4-44-4-2-444-4-2-2-22222000000002-2-2200−2i32i300002i3−2i300000000000000000000000000000000
χ6244-4-44-4-2-444-4-2-2-22222000000002-2-22002i3−2i30000−2i32i300000000000000000000000000000000
χ6344-4-4-44-24-44-422-22-2-22004i−4i4i−4i00-22-22000000−2i2i0000−2i2i0000000000000000000000000000
χ6444-4-4-44-24-44-422-22-2-2200−4i4i−4i4i00-22-220000002i−2i00002i−2i0000000000000000000000000000
χ6544-4-4-44-2-44-4422-22-2-22004i−4i−4i4i002-22-2000000−2i2i00002i−2i0000000000000000000000000000
χ6644-4-4-44-2-44-4422-22-2-2200−4i4i4i−4i002-22-20000002i−2i0000−2i2i0000000000000000000000000000
χ678-88-8008000000-8800-8000000000000000000000000000000000000000000000000000000
χ688-88-800-40000−4i34i34-4−4i34i34000000000000000000000000000000000000000000000000000000
χ698-88-800-400004i3−4i34-44i3−4i34000000000000000000000000000000000000000000000000000000
χ708-8-88008000000-8-8008000000000000000000000000000000000000000000000000000000
χ718-8-8800-40000−4i34i3444i3−4i3-4000000000000000000000000000000000000000000000000000000
χ728-8-8800-400004i3−4i344−4i34i3-4000000000000000000000000000000000000000000000000000000

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