Finite Group Databasebeta

← Group #10691721

Character table — Group #10691721

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222244444444444444444888888888888121212121616161616161616161616162424242424242424242424242424
order12222234444446664446688881212121212121212881212242424242424242488884488121212122424242422448888888888
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
χ5111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ91111111-1-1-1-1-1-11111-1111ii−i−i11-1-1-1-1-1-1i−i1-1iiii−i−i−i−iii−i−i1-1i−i11-1-1ii−i−i1-11-1ii−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−ii-1-111−i−iii1-11-1−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−iii1-1i−i11-1-1ii−i−i-11-11−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−ii-1-111−i−iii-11-11ii−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−i1-1−ii11-1-1−i−iii-11-11ii−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-11i−i-1-111ii−i−i-11-11−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−iii1-1−ii11-1-1−i−iii1-11-1−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-11i−i-1-111ii−i−i1-11-1ii−i−i−ii-1-111
χ1722222222-2-2-22-2222-22-2222i2i−2i−2i-2-222-2-2-2-2−2i2i-222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ1822222222-2-2-22-2222-22-222−2i−2i2i2i-2-222-2-2-2-22i−2i-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ192222222-2222-22222-2-2-2222222-2-2-2-22222-2-2-2-222-2-2-2-222000000000000000000000000000000
χ202222222-2222-22222-2-2-222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2000000000000000000000000000000
χ21222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-21111111100000000000000
χ23222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-2-2-1-1-1-1111100000000000000
χ24222222-1222222-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2221111-1-1-1-100000000000000
χ25222222-12-2-2-22-2-1-1-1-22-2-1-12i2i−2i−2i11-1-11111−2i2i1-1−i−iii−i−iii00000000−i3i3−i3i33−33−300000000000000
χ26222222-12-2-2-22-2-1-1-1-22-2-1-12i2i−2i−2i11-1-11111−2i2i1-1−i−iii−i−iii00000000i3−i3i3−i3−33−3300000000000000
χ27222222-12-2-2-22-2-1-1-1-22-2-1-1−2i−2i2i2i11-1-111112i−2i1-1ii−i−iii−i−i00000000−i3i3−i3i3−33−3300000000000000
χ28222222-12-2-2-22-2-1-1-1-22-2-1-1−2i−2i2i2i11-1-111112i−2i1-1ii−i−iii−i−i00000000i3−i3i3−i33−33−300000000000000
χ29222222-1-2222-22-1-1-1-2-2-2-1-122221111-1-1-1-1-2-211-1-11111-1-100000000−i3i3i3−i3−i3i3i3−i300000000000000
χ30222222-1-2222-22-1-1-1-2-2-2-1-122221111-1-1-1-1-2-211-1-11111-1-100000000i3−i3−i3i3i3−i3−i3i300000000000000
χ31222222-1-2222-22-1-1-1-2-2-2-1-1-2-2-2-21111-1-1-1-1221111-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i300000000000000
χ32222222-1-2222-22-1-1-1-2-2-2-1-1-2-2-2-21111-1-1-1-1221111-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i300000000000000
χ33222222-1-2-2-2-2-2-2-1-1-12-22-1-12i2i−2i−2i-1-11111112i−2i-11−i−i−i−iiiii00002-22i−2i-1-111−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−iiiii0000-22−2i2i11-1-1ii−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−i00002-2−2i2i-1-111ii−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−i0000-222i−2i11-1-1−i−iii00000000000000
χ372222-2-2222-222-2222-2-22-2-20000-2-2222-2-22002-200000000000000000000000022-2-20000000000
χ382222-2-2222-222-2222-2-22-2-20000-2-2222-2-22002-2000000000000000000000000-2-2220000000000
χ392222-2-222-22-2222222-2-2-2-200002222-222-200-2-200000000222200000000000000000000-2-20000
χ402222-2-222-22-2222222-2-2-2-200002222-222-200-2-200000000-2-2-2-200000000000000000000220000
χ412222-2-22-22-22-2-222222-2-2-2000022-2-22-2-2200-22000000002i2i−2i−2i00000000000000000000−2i2i0000
χ422222-2-22-22-22-2-222222-2-2-2000022-2-22-2-2200-2200000000−2i−2i2i2i000000000000000000002i−2i0000
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
χ452-2-222-22022-20-2-2-220002-22i−2i2i−2i000022-2-200002i−2i00002i−2i00000000000000000000−i2i2−i2i2002−22−2
χ462-2-222-22022-20-2-2-220002-22i−2i2i−2i000022-2-200002i−2i00002i−2i00000000000000000000i2−i2i2−i200−22−22
χ472-2-222-22022-20-2-2-220002-2−2i2i−2i2i000022-2-20000−2i2i0000−2i2i00000000000000000000−i2i2−i2i200−22−22
χ482-2-222-22022-20-2-2-220002-2−2i2i−2i2i000022-2-20000−2i2i0000−2i2i00000000000000000000i2−i2i2−i2002−22−2
χ492-2-222-220-2-2202-2-220002-22-2-220000-2-22200002-20000-22000000000000000000002−2−2200−222−2
χ502-2-222-220-2-2202-2-220002-22-2-220000-2-22200002-20000-2200000000000000000000−222−2002−2−22
χ512-2-222-220-2-2202-2-220002-2-222-20000-2-2220000-2200002-2000000000000000000002−2−22002−2−22
χ522-2-222-220-2-2202-2-220002-2-222-20000-2-2220000-2200002-200000000000000000000−222−200−222−2
χ534444-4-4-244-444-4-2-2-2-4-4422000022-2-2-222-200-2200000000000000000000000000000000000000
χ544444-4-4-24-44-444-2-2-24-4-4220000-2-2-2-22-2-22002200000000000000000000000000000000000000
χ554444-4-4-2-44-44-4-4-2-2-244-4220000-2-222-222-2002-200000000000000000000000000000000000000
χ564444-4-4-2-4-44-4-44-2-2-2-44422000022222-2-2200-2-200000000000000000000000000000000000000
χ5744-4-40044000-404-4-4000000000004-4000000000000000022−2222−2200000000000000000000000000
χ5844-4-40044000-404-4-4000000000004-40000000000000000−2222−222200000000000000000000000000
χ5944-4-4004-4000404-4-400000000000-440000000000000000−2i22i22i2−2i200000000000000000000000000
χ6044-4-4004-4000404-4-400000000000-4400000000000000002i2−2i2−2i22i200000000000000000000000000
χ614-4-444-4-2044-40-422-2000-224i−4i4i−4i0000-2-2220000−2i2i0000−2i2i000000000000000000000000000000
χ624-4-444-4-2044-40-422-2000-22−4i4i−4i4i0000-2-22200002i−2i00002i−2i000000000000000000000000000000
χ634-4-444-4-20-4-440422-2000-224-4-44000022-2-20000-2200002-2000000000000000000000000000000
χ644-4-444-4-20-4-440422-2000-22-444-4000022-2-200002-20000-22000000000000000000000000000000
χ654-4-44-44404-4-404-4-44000-44000000004-44-4000000000000000000000000000000000000000000
χ664-4-44-4440-4440-4-4-44000-4400000000-44-44000000000000000000000000000000000000000000
χ674-4-44-44-204-4-40422-20002-200000000-22-2200000023−2323−2300000000000000000000000000000000
χ684-4-44-44-204-4-40422-20002-200000000-22-22000000−2323−232300000000000000000000000000000000
χ694-4-44-44-20-4440-422-20002-2000000002-22-2000000−2i32i32i3−2i300000000000000000000000000000000
χ704-4-44-44-20-4440-422-20002-2000000002-22-20000002i3−2i3−2i32i300000000000000000000000000000000
χ7188-8-800-48000-80-44400000000000-440000000000000000000000000000000000000000000000
χ7288-8-800-4-800080-444000000000004-40000000000000000000000000000000000000000000000
χ738-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ748-88-800-40000004-44000000000−4i34i3000000000000000000000000000000000000000000000000
χ758-88-800-40000004-440000000004i3−4i3000000000000000000000000000000000000000000000000

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