Finite Group Databasebeta

← Group #10780328

Character table — Group #10780328

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222244444444444444444448888888888881212121216161616161616161616161624242424242448484848
order122234444666244446688881212121212121212881212242424242424242488882444661212121212122444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111
χ71111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ9111111111111-11-1-1-1-1-111-1-111-1-111111-1-1-11111-1-1-1-111111-11-111-1-111-1-11-11-1-1-1-111-1
χ10111111111111-11-1-1-1-1-111-1-111-1-111111-1-1-11111-1-1-1-11111-11-11-1-111-1-1111-11-1-1-11-1-11
χ11111111111111-11-1-1-1-1-111-1-111-1-111111-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-11-11111-1-11
χ12111111111111-11-1-1-1-1-111-1-111-1-111111-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-11-1111-111-1
χ13111111111111-11-1-1-1-1-1-1-11111-1-11111-11-1-1-1-1-1-1111111111-1-1111-1-1-1-111-11-11-1-1-11-11
χ14111111111111-11-1-1-1-1-1-1-11111-1-11111-11-1-1-1-1-1-111111111-111-1-1-11111-1-1-11-11-1-11-11-1
χ15111111111111-11-1-1-1-1-1-1-11111-1-11111-11-1-1-1-1-1-11111-1-1-1-11-1-1111-1-1-1-1111-11-1111-11-1
χ16111111111111-11-1-1-1-1-1-1-11111-1-11111-11-1-1-1-1-1-11111-1-1-1-1-111-1-1-11111-1-11-11-111-11-11
χ17222222-2-222222-2-2-22220000-2-2-2-222-2-200-2200000000000000000000000022-2-2000000
χ18222222-2-222222-2-2-22220000-2-2-2-222-2-200-22000000000000000000000000-2-222000000
χ19222222-2-22222-2-222-2-2-20000-2-22222-2-2002-20000000000000000000000002-2-22000000
χ20222222-2-22222-2-222-2-2-20000-2-22222-2-2002-2000000000000000000000000-222-2000000
χ2122222-222-22222-2-22-22222-2-2-2-222-2-222-22-2-222-2-222-2-200000000000000000000000000
χ2222222-222-22222-2-22-222-2-222-2-222-2-2222-2-2-2-2-222-2-22200000000000000000000000000
χ2322222-222-2222-2-22-22-2-22222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000000000
χ2422222-222-2222-2-22-22-2-2-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-200000000000000000000000000
χ2522222-2-2-2-2222222-2-222000022-2-2-2-2-2-2002-2000000002i2i−2i−2i00000000000000002i−2i0000
χ2622222-2-2-2-2222222-2-222000022-2-2-2-2-2-2002-200000000−2i−2i2i2i0000000000000000−2i2i0000
χ2722222-2-2-2-2222-22-222-2-200002222-2-2-2-200-22000000002i2i−2i−2i0000000000000000−2i2i0000
χ2822222-2-2-2-2222-22-222-2-200002222-2-2-2-200-2200000000−2i−2i2i2i00000000000000002i−2i0000
χ292222-12222-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-10000000000
χ302222-12222-1-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2111111110000000000
χ312222-12222-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-111111111000022-2-2-1-1-1-111110000000000
χ322222-12222-1-1-122222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2-1-1111111110000-2-2221111-1-1-1-10000000000
χ332222-12222-1-1-1-22-2-2-21122-2-2-1-111-1-1-1-12-211-1-1-1-1111100002-22-2-1-111-1-1110000000000
χ342222-12222-1-1-1-22-2-2-21122-2-2-1-111-1-1-1-12-211-1-1-1-111110000-22-2211-1-111-1-10000000000
χ352222-12222-1-1-1-22-2-2-211-2-222-1-111-1-1-1-1-22111111-1-1-1-100002-2-22-1-11111-1-10000000000
χ362222-12222-1-1-1-22-2-2-211-2-222-1-111-1-1-1-1-22111111-1-1-1-10000-222-211-1-1-1-1110000000000
χ372222-1-222-2-1-1-12-2-22-2-1-122-2-211-1-111-1-1-2211-1-111-1-11100000000−i3i3−i3i3−i3i3−i3i30000000000
χ382222-1-222-2-1-1-12-2-22-2-1-122-2-211-1-111-1-1-2211-1-111-1-11100000000i3−i3i3−i3i3−i3i3−i30000000000
χ392222-1-222-2-1-1-12-2-22-2-1-1-2-22211-1-111-1-12-21111-1-111-1-100000000−i3i3−i3i3i3−i3i3−i30000000000
χ402222-1-222-2-1-1-12-2-22-2-1-1-2-22211-1-111-1-12-21111-1-111-1-100000000i3−i3i3−i3−i3i3−i3i30000000000
χ412222-1-222-2-1-1-1-2-22-22112222111111-1-1-2-2-1-1-1-11111-1-100000000−i3i3i3−i3−i3i3i3−i30000000000
χ422222-1-222-2-1-1-1-2-22-22112222111111-1-1-2-2-1-1-1-11111-1-100000000i3−i3−i3i3i3−i3−i3i30000000000
χ432222-1-222-2-1-1-1-2-22-2211-2-2-2-2111111-1-122-1-111-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i30000000000
χ442222-1-222-2-1-1-1-2-22-2211-2-2-2-2111111-1-122-1-111-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i30000000000
χ454444-24-4-44-2-2-24-4-4-44-2-200002222-2-222002-20000000000000000000000000000000000
χ464444-24-4-44-2-2-2-4-444-422000022-2-2-2-22200-220000000000000000000000000000000000
χ474444-2-4-4-4-4-2-2-2444-4-4-2-20000-2-222222200-220000000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-2-44-444220000-2-2-2-22222002-20000000000000000000000000000000000
χ494-44-4404-40-44-40000000004i−4i0000004-400000000004i−4i00000000000000000000000000
χ504-44-4404-40-44-4000000000−4i4i0000004-40000000000−4i4i00000000000000000000000000
χ514-44-440-440-44-400000004i−4i00000000-4400004i−4i00000000000000000000000000000000
χ524-44-440-440-44-40000000−4i4i00000000-440000−4i4i00000000000000000000000000000000
χ534-44-4-204-402-2200000−2i32i3004i−4i00−2i32i300-2200000023−2300−2i2i00000000000000000000000000
χ544-44-4-204-402-2200000−2i32i300−4i4i00−2i32i300-22000000−2323002i−2i00000000000000000000000000
χ554-44-4-204-402-22000002i3−2i3004i−4i002i3−2i300-22000000−232300−2i2i00000000000000000000000000
χ564-44-4-204-402-22000002i3−2i300−4i4i002i3−2i300-2200000023−23002i−2i00000000000000000000000000
χ574-44-4-20-4402-2200000−2i32i34i−4i00002i3−2i3002-20000−2i2i0023−230000000000000000000000000000
χ584-44-4-20-4402-2200000−2i32i3−4i4i00002i3−2i3002-200002i−2i00−23230000000000000000000000000000
χ594-44-4-20-4402-22000002i3−2i34i−4i0000−2i32i3002-20000−2i2i00−23230000000000000000000000000000
χ604-44-4-20-4402-22000002i3−2i3−4i4i0000−2i32i3002-200002i−2i0023−230000000000000000000000000000
χ614-4-444400-4-4-440000000000000004-400000000000000−2i22i2−2i22i20000000000000000000000
χ624-4-444400-4-4-440000000000000004-4000000000000002i2−2i22i2−2i20000000000000000000000
χ634-4-444-4004-4-44000000000000000-440000000000000022−22−22220000000000000000000000
χ644-4-444-4004-4-44000000000000000-4400000000000000−222222−220000000000000000000000
χ6588-8-8800008-8-8000000000000000000000000000000000000000000000000000000000
χ6688-8-8-40000-44400000000000−4i34i300000000000000000000000000000000000000000000
χ6788-8-8-40000-444000000000004i3−4i300000000000000000000000000000000000000000000
χ688-8-88-4800-844-4000000000000000-440000000000000000000000000000000000000000
χ698-8-88-4-800844-40000000000000004-40000000000000000000000000000000000000000

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