Finite Group Databasebeta

← Group #10691742

Character table — Group #10691742

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order1222223444444666444668888121212121212121288121224242424242424248888226666882424242444448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ91111111-1-1-1-1-1-11111-1111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−iii−i−i1-111-1-1i−iii−i−i11-1-1ii−i−ii−i11-1-1
χ101111111-1-1-1-1-1-11111-1111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−iii−i−i-11-1-111−ii−i−iii11-1-1−i−iiii−i-1-111
χ111111111-1-1-1-1-1-11111-1111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−i−i−iii1-111-1-1i−iii−i−i-1-111−i−iii−ii-1-111
χ121111111-1-1-1-1-1-11111-1111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−i−i−iii-11-1-111−ii−i−iii-1-111ii−i−i−ii11-1-1
χ131111111-1-1-1-1-1-11111-1111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiiiii−i−i1-111-1-1−ii−i−iii-1-111ii−i−ii−i-1-111
χ141111111-1-1-1-1-1-11111-1111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiiiii−i−i-11-1-111i−iii−i−i-1-111−i−iiii−i11-1-1
χ151111111-1-1-1-1-1-11111-1111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiii−i−iii1-111-1-1−ii−i−iii11-1-1−i−iii−ii11-1-1
χ161111111-1-1-1-1-1-11111-1111−i−iii11-1-1-1-1-1-1−ii1-1−i−i−i−iiiii−i−iii-11-1-111i−iii−i−i11-1-1ii−i−i−ii-1-111
χ1722222222-222-22222-2-2-2222222-2-22-2-2222-2-2-2-222-2-222-2-2000000000000000000000000000000
χ1822222222-222-22222-2-2-222-2-2-2-2-2-22-2-222222-2-2-2-222-2-222000000000000000000000000000000
χ192222222-22-2-22-2222-22-2222i2i−2i−2i-2-2-222-2-2-2−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ202222222-22-2-22-2222-22-222−2i−2i2i2i-2-2-222-2-2-22i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ21222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000022-1-1-1-122-1-1-1-100000000000000
χ22222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-21111-2-2111100000000000000
χ23222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-1-1-1-1-2-2111100000000000000
χ24222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2111122-1-1-1-100000000000000
χ25222222-12-222-22-1-1-1-2-2-2-1-1222211-111-1-1-1-2-211-1-111-1-111000000−i3i3−i3i300−i3i3−i3i300000000000000
χ26222222-12-222-22-1-1-1-2-2-2-1-1222211-111-1-1-1-2-211-1-111-1-111000000i3−i3i3−i300i3−i3i3−i300000000000000
χ27222222-12-222-22-1-1-1-2-2-2-1-1-2-2-2-211-111-1-1-1221111-1-111-1-1000000−i3i3−i3i300i3−i3i3−i300000000000000
χ28222222-12-222-22-1-1-1-2-2-2-1-1-2-2-2-211-111-1-1-1221111-1-111-1-1000000i3−i3i3−i300−i3i3−i3i300000000000000
χ29222222-1-22-2-22-2-1-1-1-22-2-1-12i2i−2i−2i111-1-1111−2i2i1-1−i−iiiii−i−i000000−i3i3i3−i3003−3−3300000000000000
χ30222222-1-22-2-22-2-1-1-1-22-2-1-12i2i−2i−2i111-1-1111−2i2i1-1−i−iiiii−i−i000000i3−i3−i3i300−333−300000000000000
χ31222222-1-22-2-22-2-1-1-1-22-2-1-1−2i−2i2i2i111-1-11112i−2i1-1ii−i−i−i−iii000000−i3i3i3−i300−333−300000000000000
χ32222222-1-22-2-22-2-1-1-1-22-2-1-1−2i−2i2i2i111-1-11112i−2i1-1ii−i−i−i−iii000000i3−i3−i3i3003−3−3300000000000000
χ33222222-1-2-2-2-2-2-2-1-1-12-22-1-12i2i−2i−2i-1-11111112i−2i-11−i−i−i−iiiii00002-2-1-1112i−2i−i−iii00000000000000
χ34222222-1-2-2-2-2-2-2-1-1-12-22-1-12i2i−2i−2i-1-11111112i−2i-11−i−i−i−iiiii0000-2211-1-1−2i2iii−i−i00000000000000
χ35222222-1-2-2-2-2-2-2-1-1-12-22-1-1−2i−2i2i2i-1-1111111−2i2i-11iiii−i−i−i−i00002-2-1-111−2i2iii−i−i00000000000000
χ36222222-1-2-2-2-2-2-2-1-1-12-22-1-1−2i−2i2i2i-1-1111111−2i2i-11iiii−i−i−i−i0000-2211-1-12i−2i−i−iii00000000000000
χ372222-2-2222-222-2222-2-22-2-20000-2-2222-2-22002-20000000000000000000000002-22-20000000000
χ382222-2-2222-222-2222-2-22-2-20000-2-2222-2-22002-2000000000000000000000000-22-220000000000
χ392222-2-222-2-22-2-222222-2-2-20000222-2-2-2-2200-22000000002i2i−2i−2i00000000000000000000−2i2i0000
χ402222-2-222-2-22-2-222222-2-2-20000222-2-2-2-2200-2200000000−2i−2i2i2i000000000000000000002i−2i0000
χ412222-2-22-222-2222222-2-2-2-2000022-22222-200-2-200000000222200000000000000000000-2-20000
χ422222-2-22-222-2222222-2-2-2-2000022-22222-200-2-200000000-2-2-2-200000000000000000000220000
χ432222-2-22-2-22-2-22222-222-2-20000-2-2-2-2-222-200220000000000000000000000002-2-220000000000
χ442222-2-22-2-22-2-22222-222-2-20000-2-2-2-2-222-20022000000000000000000000000-222-20000000000
χ4522-2-22-2220-2-2022-2-20002-22i−2i2i−2i002002-2-200002i−2i002i−2i00000000000000000000002−22−200−i2i2−i2i2
χ4622-2-22-2220-2-2022-2-20002-22i−2i2i−2i002002-2-200002i−2i002i−2i0000000000000000000000−22−2200i2−i2i2−i2
χ4722-2-22-2220-2-2022-2-20002-2−2i2i−2i2i002002-2-20000−2i2i00−2i2i00000000000000000000002−22−200i2−i2i2−i2
χ4822-2-22-2220-2-2022-2-20002-2−2i2i−2i2i002002-2-20000−2i2i00−2i2i0000000000000000000000−22−2200−i2i2−i2i2
χ4922-2-22-22-20220-22-2-20002-22-2-2200-200-22200002-200-220000000000000000000000−i2i2i2−i200−i2i2i2−i2
χ5022-2-22-22-20220-22-2-20002-22-2-2200-200-22200002-200-220000000000000000000000i2−i2−i2i200i2−i2−i2i2
χ5122-2-22-22-20220-22-2-20002-2-222-200-200-2220000-22002-20000000000000000000000−i2i2i2−i200i2−i2−i2i2
χ5222-2-22-22-20220-22-2-20002-2-222-200-200-2220000-22002-20000000000000000000000i2−i2−i2i200−i2i2i2−i2
χ534444-4-4-244-444-4-2-2-2-4-4422000022-2-2-222-200-2200000000000000000000000000000000000000
χ544444-4-4-24-4-44-4-4-2-2-244-4220000-2-2-22222-2002-200000000000000000000000000000000000000
χ554444-4-4-2-444-444-2-2-24-4-4220000-2-22-2-2-2-22002200000000000000000000000000000000000000
χ564444-4-4-2-4-44-4-44-2-2-2-44422000022222-2-2200-2-200000000000000000000000000000000000000
χ5744-4-44-4-240-4-404-222000-224i−4i4i−4i00-200-2220000−2i2i00−2i2i00000000000000000000000000000000
χ5844-4-44-4-240-4-404-222000-22−4i4i−4i4i00-200-22200002i−2i002i−2i00000000000000000000000000000000
χ5944-4-44-4-2-40440-4-222000-224-4-44002002-2-20000-22002-200000000000000000000000000000000
χ6044-4-44-4-2-40440-4-222000-22-444-4002002-2-200002-200-2200000000000000000000000000000000
χ6144-4-4-444404-40-44-4-4000-44000000400-44-4000000000000000000000000000000000000000000
χ6244-4-4-444-40-44044-4-4000-44000000-4004-44000000000000000000000000000000000000000000
χ6344-4-4-44-2404-40-4-2220002-2000000-2002-2200000023−230023−23000000000000000000000000000000
χ6444-4-4-44-2404-40-4-2220002-2000000-2002-22000000−232300−2323000000000000000000000000000000
χ6544-4-4-44-2-40-4404-2220002-2000000200-22-2000000−2i32i3002i3−2i3000000000000000000000000000000
χ6644-4-4-44-2-40-4404-2220002-2000000200-22-20000002i3−2i300−2i32i3000000000000000000000000000000
χ674-44-40040400-40-44-40000000000004-4000000000000000−2i22i2−2i22i200000000000000000000000000
χ684-44-40040400-40-44-40000000000004-40000000000000002i2−2i22i2−2i200000000000000000000000000
χ694-44-40040-40040-44-4000000000000-4400000000000000022−22−222200000000000000000000000000
χ704-44-40040-40040-44-4000000000000-44000000000000000−222222−2200000000000000000000000000
χ718-88-800-40800-804-44000000000000-44000000000000000000000000000000000000000000000
χ728-88-800-40-800804-440000000000004-4000000000000000000000000000000000000000000000
χ738-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400000044-4000000000−4i34i3000000000000000000000000000000000000000000000000
χ758-8-8800-400000044-40000000004i3−4i3000000000000000000000000000000000000000000000000

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