Finite Group Databasebeta

← Group #10706113

Character table — Group #10706113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881616161616161616161616162424242424242424242424244848
order122222344666444444444661212121212121212246612121212121212128888242424242424242444448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1111iiii−i−i−i−i-1-1
χ6111111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1−i−i−i−iiiii11
χ7111111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1111−i−i−i−iiiii-1-1
χ8111111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1iiii−i−i−i−i11
χ91111111-1-1111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1i−ii−iii−i−iii−i−i11-1-1ii−i−iii−i−i1-1
χ101111111-1-1111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1i−ii−iii−i−iii−i−i-1-111−i−iii−i−iii-11
χ111111111-1-1111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1−ii−ii−i−iii−i−iii11-1-1−i−iii−i−iii1-1
χ121111111-1-1111-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1−ii−ii−i−iii−i−iii-1-111ii−i−iii−i−i-11
χ131111111-1-1111-1-1-1-1-1111111-1-1-1-11111-11-1-111-1-1-1-1111-1-1111-1-1-1-11111-1-111-1-1-1-111-11
χ141111111-1-1111-1-1-1-1-1111111-1-1-1-11111-11-1-111-1-1-1-1111-1-1111-1-1-1-111-1-111-1-11111-1-11-1
χ151111111-1-1111-1-1-1-1-1111111-1-1-1-11111-11-1-111-1-1-1-111-111-1-1-11111-1-111-1-1-1-11111-1-1-11
χ161111111-1-1111-1-1-1-1-1111111-1-1-1-11111-11-1-111-1-1-1-111-111-1-1-11111-1-1-1-11111-1-1-1-1111-1
χ172222222222222-2-222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ182222222222222-2-2-2-222-2-222222222222-222-2-2-2-2-2-2-2-200000000000000000000000000
χ192222222-2-2222-2222222-2-222-2-2-2-22222-2-2-2-2-2-22222-2-200000000000000000000000000
χ202222222-2-2222-222-2-2-2-22222-2-2-2-2-2-2-2-22-222-2-222-2-22200000000000000000000000000
χ21222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-1222222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ23222222-122-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-11111-2211-1-1-1-111112i2i−2i−2i−i−i−i−iiiii00000000000000
χ24222222-122-1-1-1222-2-2-2-2-2-2-1-1-1-1-1-11111-2211-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i00000000000000
χ25222222-122-1-1-12-2-222-2-222-1-1-1-1-1-11111-2-2111111-1-1-1-100003−33−33−33−300000000000000
χ26222222-122-1-1-12-2-222-2-222-1-1-1-1-1-11111-2-2111111-1-1-1-10000−33−33−33−3300000000000000
χ27222222-122-1-1-12-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-12-2-1-1111111110000−i3i3−i3i3i3−i3i3−i300000000000000
χ28222222-122-1-1-12-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-12-2-1-1111111110000i3−i3i3−i3−i3i3−i3i300000000000000
χ29222222-1-2-2-1-1-1-2222222-2-2-1-11111-1-1-1-1-2-21111-1-1-1-1110000−i3i3i3−i3−i3i3i3−i300000000000000
χ30222222-1-2-2-1-1-1-2222222-2-2-1-11111-1-1-1-1-2-21111-1-1-1-1110000i3−i3−i3i3i3−i3−i3i300000000000000
χ31222222-1-2-2-1-1-1-222-2-2-2-222-1-1111111112-2-1-111-1-111-1-100003−3−33−333−300000000000000
χ32222222-1-2-2-1-1-1-222-2-2-2-222-1-1111111112-2-1-111-1-111-1-10000−333−33−3−3300000000000000
χ33222222-1-2-2-1-1-1-2-2-222-2-2-2-2-1-11111111122-1-1-1-111-1-1112i−2i2i−2i−i−iii−i−iii00000000000000
χ34222222-1-2-2-1-1-1-2-2-222-2-2-2-2-1-11111111122-1-1-1-111-1-111−2i2i−2i2iii−i−iii−i−i00000000000000
χ35222222-1-2-2-1-1-1-2-2-2-2-22222-1-11111-1-1-1-1-2211-1-11111-1-12-2-22-1-11111-1-100000000000000
χ36222222-1-2-2-1-1-1-2-2-2-2-22222-1-11111-1-1-1-1-2211-1-11111-1-1-222-211-1-1-1-11100000000000000
χ372-22-22-22002-2-202i−2i2i−2i2-2002-2000022-2-20000002i−2i2i−2i0000000000000000002−2−i2i2−i2i22−200
χ382-22-22-22002-2-202i−2i2i−2i2-2002-2000022-2-20000002i−2i2i−2i000000000000000000−22i2−i2i2−i2−2200
χ392-22-22-22002-2-202i−2i−2i2i-22002-20000-2-2220000002i−2i−2i2i000000000000000000−i2i2−222−2i2−i200
χ402-22-22-22002-2-202i−2i−2i2i-22002-20000-2-2220000002i−2i−2i2i000000000000000000i2−i22−2−22−i2i200
χ412-22-22-22002-2-20−2i2i2i−2i-22002-20000-2-222000000−2i2i2i−2i000000000000000000−i2i22−2−22i2−i200
χ422-22-22-22002-2-20−2i2i2i−2i-22002-20000-2-222000000−2i2i2i−2i000000000000000000i2−i2−222−2−i2i200
χ432-22-22-22002-2-20−2i2i−2i2i2-2002-2000022-2-2000000−2i2i−2i2i0000000000000000002−2i2−i2i2−i22−200
χ442-22-22-22002-2-20−2i2i−2i2i2-2002-2000022-2-2000000−2i2i−2i2i000000000000000000−22−i2i2−i2i2−2200
χ454444-4-4444444-400000000-4-444-4-4000000000000000000000000000000000000000000
χ464444-4-44-4-4444400000000-4-4-4-444000000000000000000000000000000000000000000
χ474444-4-4-244-2-2-2-40000000022-2-222−2i32i3−2i32i300−2i32i30000000000000000000000000000000000
χ484444-4-4-244-2-2-2-40000000022-2-2222i3−2i32i3−2i3002i3−2i30000000000000000000000000000000000
χ494444-4-4-2-4-4-2-2-24000000002222-2-2−2i32i3−2i32i3002i3−2i30000000000000000000000000000000000
χ504444-4-4-2-4-4-2-2-24000000002222-2-22i3−2i32i3−2i300−2i32i30000000000000000000000000000000000
χ514-44-44-4-200-22204i−4i4i−4i4-400-220000-2-222000000−2i2i−2i2i0000000000000000000000000000
χ524-44-44-4-200-22204i−4i−4i4i-4400-22000022-2-2000000−2i2i2i−2i0000000000000000000000000000
χ534-44-44-4-200-2220−4i4i4i−4i-4400-22000022-2-20000002i−2i−2i2i0000000000000000000000000000
χ544-44-44-4-200-2220−4i4i−4i4i4-400-220000-2-2220000002i−2i2i−2i0000000000000000000000000000
χ554-44-4-444004-4-400000004i−4i-440000000000000000004i−4i00000000000000000000000000
χ564-44-4-444004-4-40000000−4i4i-44000000000000000000−4i4i00000000000000000000000000
χ574-44-4-44-200-22200000004i−4i2-20000−2i32i32i3−2i3000023−230000−2i2i00000000000000000000000000
χ584-44-4-44-200-22200000004i−4i2-200002i3−2i3−2i32i30000−23230000−2i2i00000000000000000000000000
χ594-44-4-44-200-2220000000−4i4i2-20000−2i32i32i3−2i30000−232300002i−2i00000000000000000000000000
χ604-44-4-44-200-2220000000−4i4i2-200002i3−2i3−2i32i3000023−2300002i−2i00000000000000000000000000
χ614-4-440044i−4i-44-4000000000004i−4i0000000000000000000000000000002-22i−2i0000000000
χ624-4-440044i−4i-44-4000000000004i−4i000000000000000000000000000000-22−2i2i0000000000
χ634-4-44004−4i4i-44-400000000000−4i4i0000000000000000000000000000002-2−2i2i0000000000
χ644-4-44004−4i4i-44-400000000000−4i4i000000000000000000000000000000-222i−2i0000000000
χ6588-8-800800-8-88000000000000000000000000000000000000000000000000000000000
χ6688-8-800-40044-4000000000000043−43000000000000000000000000000000000000000000
χ6788-8-800-40044-40000000000000−4343000000000000000000000000000000000000000000
χ688-8-8800-48i−8i4-4400000000000−4i4i00000000000000000000000000000000000000000000
χ698-8-8800-4−8i8i4-44000000000004i−4i00000000000000000000000000000000000000000000

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