Finite Group Databasebeta

← Group #10691201

Character table — Group #10691201

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order1222223444466666662244444412121212446612121212121212121212444412121212121212128888888888888888
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
χ5111111111111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-11111111-1-11111-1-1-1-1-1-11-1-1-1111111-1-1-1-11-1-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-11111111-1-11111-1-1-1-1-1-11-1-1-1111111-1-1-1-11-1-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-11111111-1-11111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-111-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-11111111-1-11111-1-1-1-1-1-11-1-1-1111111-1-1-1-1-111-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-222-2-22222-2-222-2-222-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2220000000000000000000000000000
χ192222222-2-2-2-2222222222-2-2-2-222-2-2-2-22-222-2-2-2-22222-2-20000000000000000000000000000
χ202222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-22-2-2-2-222-2-222220000000000000000000000000000
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
χ23222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-2-2-1-111-1-11111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-2-2-1-111-1-11111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-2-211-1-11111-1-11122-2-21111-1-1-1-10000000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-1-1-1-2-211-1-11111-1-111-2-222-1-1-1-111110000000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122111111-1-111-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122111111-1-111-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-22-1-1-1-1111111-1-12-22-2-1-111-1-1110000000000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-22-1-1-1-1111111-1-1-22-2211-1-111-1-10000000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211112-2-1-11111-1-1-1-1110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-122-2-2-2-22211112-2-1-11111-1-1-1-1110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211112-211-1-1-1-1-1-111112-2-2211-1-1-1-1110000000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-1-2-22222-2-211112-211-1-1-1-1-1-11111-222-2-1-11111-1-10000000000000000
χ35222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-221111-1-111-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ36222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-221111-1-111-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ372222-2-2222-2-2-2-222-2-22002-2002-222-2-200002-200002-20000000000000000002i−2i2i−2i00000000
χ382222-2-2222-2-2-2-222-2-22002-2002-222-2-200002-200002-2000000000000000000−2i2i−2i2i00000000
χ392222-2-2222-2-2-2-222-2-2200-2200-2222-2-20000-220000-22000000000000002i−2i2i−2i000000000000
χ402222-2-2222-2-2-2-222-2-2200-2200-2222-2-20000-220000-2200000000000000−2i2i−2i2i000000000000
χ412222-2-22-2-222-2-222-2-22002-200-22-2-22200002-20000-220000000000000000002-2-2200000000
χ422222-2-22-2-222-2-222-2-22002-200-22-2-22200002-20000-22000000000000000000-222-200000000
χ432222-2-22-2-222-2-222-2-2200-22002-2-2-2220000-2200002-2000000000000002-2-22000000000000
χ442222-2-22-2-222-2-222-2-2200-22002-2-2-2220000-2200002-200000000000000-222-2000000000000
χ4522-2-22-222-22-2222-2-2-2-22-2002-2002-22-2002-2002-2000000000000000000000000002−22−22−22−2
χ4622-2-22-222-22-2222-2-2-2-22-2002-2002-22-2002-2002-200000000000000000000000000−22−22−22−22
χ4722-2-22-222-22-2222-2-2-2-2-2200-22002-22-200-2200-22000000000000000000000000002−22−2−22−22
χ4822-2-22-222-22-2222-2-2-2-2-2200-22002-22-200-2200-2200000000000000000000000000−22−222−22−2
χ4922-2-22-22-22-22222-2-2-2-22-200-2200-22-22002-200-2200000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ5022-2-22-22-22-22222-2-2-2-22-200-2200-22-22002-200-2200000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ5122-2-22-22-22-22222-2-2-2-2-22002-200-22-2200-22002-200000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ5222-2-22-22-22-22222-2-2-2-2-22002-200-22-2200-22002-200000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ534444-4-4-244-4-422-2-222-2004-4004-4-2-2220000-220000-22000000000000000000000000000000
χ544444-4-4-244-4-422-2-222-200-4400-44-2-22200002-200002-2000000000000000000000000000000
χ554444-4-4-2-4-44422-2-222-2004-400-4422-2-20000-2200002-2000000000000000000000000000000
χ564444-4-4-2-4-44422-2-222-200-44004-422-2-200002-20000-22000000000000000000000000000000
χ5744-4-44-4-24-44-4-2-2-222224-4004-400-22-2200-2200-220000000000000000000000000000000000
χ5844-4-44-4-24-44-4-2-2-22222-4400-4400-22-22002-2002-20000000000000000000000000000000000
χ5944-4-44-4-2-44-44-2-2-222224-400-44002-22-200-22002-20000000000000000000000000000000000
χ6044-4-44-4-2-44-44-2-2-22222-44004-4002-22-2002-200-220000000000000000000000000000000000
χ6144-4-4-4444-4-44-4-44-444-4000000004-4-44000000000000000000000000000000000000000000
χ6244-4-4-444-444-4-4-44-444-400000000-444-4000000000000000000000000000000000000000000
χ6344-4-4-44-24-4-4422-22-2-2200000000-222-20000000023−230023−230000000000000000000000000000
χ6444-4-4-44-24-4-4422-22-2-2200000000-222-200000000−232300−23230000000000000000000000000000
χ6544-4-4-44-2-444-422-22-2-22000000002-2-220000000023−2300−23230000000000000000000000000000
χ6644-4-4-44-2-444-422-22-2-22000000002-2-2200000000−23230023−230000000000000000000000000000
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).