Finite Group Databasebeta

← Group #10831097

Character table — Group #10831097

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order124422234446888812122244666666688121212121212122424242422224444666666668812121212121212122424242424242244888844884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ9111111111111-1-1-1-11111111111111-1-11111111-1-1-1-11-11-11-11-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-11-1
χ10111111111111-1-1-1-11111111111111-1-11111111-1-1-1-11-11-11-11-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11
χ11111111111111-1-1-1-11111111111111-1-11111111-1-1-1-1-11-11-11-11-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ12111111111111-1-1-1-11111111111111-1-11111111-1-1-1-1-11-11-11-11-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1
χ13111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-11-1-111-1-1111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1111-1-11
χ14111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-11-1-111-1-1111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-111-1
χ15111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-111-1-111-1-1-11111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-111-1
χ16111111111111-1-1-1-111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-1-111-1-111-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1-11
χ172222222-1222-12222-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-12222-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111112211111111-1-1-1-1-1-10000000000000000
χ192222222-1222-12222-1-1-2-2-2-2-1-1-1111122-1-11111-1-1-1-1-122-2-222-2-2-1-1-1-11111-2-2-1-1-1-11111-1-111110000000000000000
χ202222222-1222-12222-1-1-2-2-2-2-1-1-1111122-1-11111-1-1-1-1-1-2-222-2-2221111-1-1-1-1-2-21111-1-1-1-1-1-111110000000000000000
χ212222222-1222-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-111112-22-22-22-2-1-111-1-111-2-2-1-111-1-1111111110000000000000000
χ222222222-1222-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-11111-22-22-22-2211-1-111-1-1-2-211-1-111-1-11111110000000000000000
χ232222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-11111-2-2-1-11111-111112-2-222-2-22-1-11111-1-122-1-11111-1-111-1-1-1-10000000000000000
χ242222222-1222-1-2-2-2-2-1-1-2-2-2-2-1-1-11111-2-2-1-11111-11111-222-2-222-211-1-1-1-1112211-1-1-1-11111-1-1-1-10000000000000000
χ2522222-2-22-2-2222222222-22-22-2-222-2-2-2-2-2-222-2-22222200000000000000002-200000000-2-222-2-20000000000000000
χ2622222-2-22-2-222222222-22-222-2-2-2-222-2-2-2-2-2-222222220000000000000000-2200000000-2-2-2-2220000000000000000
χ2722222-2-22-2-222-2-2-2-2222-22-22-2-222-2-222-2-222-2-22-2-2-2-20000000000000000-220000000022-2-2220000000000000000
χ2822222-2-22-2-222-2-2-2-222-22-222-2-2-2-22222-2-2-2-2222-2-2-2-200000000000000002-2000000002222-2-20000000000000000
χ2922222-2-2-1-2-22-12222-1-12-22-2-111-1-111-2-211-1-111-1-1-1-1-100000000−i3i3−i3i3−i3i3−i3i32-2−i3i3−i3i3−i3i3−i3i311-1-1110000000000000000
χ3022222-2-2-1-2-22-12222-1-12-22-2-111-1-111-2-211-1-111-1-1-1-1-100000000i3−i3i3−i3i3−i3i3−i32-2i3−i3i3−i3i3−i3i3−i311-1-1110000000000000000
χ3122222-2-2-1-2-22-12222-1-1-22-22-11111-1-1-2-21111-1-1-1-1-1-1-100000000−i3i3−i3i3i3−i3i3−i3-22−i3i3−i3i3i3−i3i3−i31111-1-10000000000000000
χ3222222-2-2-1-2-22-12222-1-1-22-22-11111-1-1-2-21111-1-1-1-1-1-1-100000000i3−i3i3−i3−i3i3−i3i3-22i3−i3i3−i3−i3i3−i3i31111-1-10000000000000000
χ3322222-2-2-1-2-22-1-2-2-2-2-1-12-22-2-111-1-1112211-1-111-1111100000000−i3i3i3−i3−i3i3i3−i3-22−i3i3i3−i3−i3i3i3−i3-1-111-1-10000000000000000
χ3422222-2-2-1-2-22-1-2-2-2-2-1-12-22-2-111-1-1112211-1-111-1111100000000i3−i3−i3i3i3−i3−i3i3-22i3−i3−i3i3i3−i3−i3i3-1-111-1-10000000000000000
χ3522222-2-2-1-2-22-1-2-2-2-2-1-1-22-22-11111-1-1221111-1-1-1111100000000−i3i3i3−i3i3−i3−i3i32-2−i3i3i3−i3i3−i3−i3i3-1-1-1-1110000000000000000
χ3622222-2-2-1-2-22-1-2-2-2-2-1-1-22-22-11111-1-1221111-1-1-1111100000000i3−i3−i3i3−i3i3i3−i32-2i3−i3−i3i3−i3i3i3−i3-1-1-1-1110000000000000000
χ3722-2-22222-2-2-220000-2-22-2-2222222-2-200-2-2-2-222-200000000000000000000000000000000000022-2-200002-2000000
χ3822-2-22222-2-2-220000-2-22-2-2222222-2-200-2-2-2-222-2000000000000000000000000000000000000-2-2220000-22000000
χ3922-2-22222-2-2-220000-2-2-222-2222-2-22200-2-222-2-2-200000000000000000000000000000000000022-2-20000-22000000
χ4022-2-22222-2-2-220000-2-2-222-2222-2-22200-2-222-2-2-2000000000000000000000000000000000000-2-22200002-2000000
χ4122-2-22-2-2222-220000-2-222-2-22-2-222220022-2-2-2-2-200000000000000000000000000000000000000002i2i−2i−2i002i−2i0000
χ4222-2-22-2-2222-220000-2-222-2-22-2-222220022-2-2-2-2-20000000000000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ4322-2-22-2-2222-220000-2-2-2-2222-2-2-2-2-2-200222222-200000000000000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ4422-2-22-2-2222-220000-2-2-2-2222-2-2-2-2-2-200222222-20000000000000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ4522-2-2-22-222-22222-2-2-2-20000-22-200002-22-20000222-2-2002200-2-200002222000000-2-2-2-22-200000000000000000000
χ4622-2-2-22-222-22222-2-2-2-20000-22-200002-22-20000222-2-200-2-200220000-2-2-2-200000022222-200000000000000000000
χ4722-2-2-22-222-222-2-222-2-20000-22-20000-222-200002-2-222002-200-22000022-2-2000000-2-222-2200000000000000000000
χ4822-2-2-22-222-222-2-222-2-20000-22-20000-222-200002-2-22200-22002-20000-2-22200000022-2-2-2200000000000000000000
χ4922-2-2-22-2-12-22-122-2-21100001-11−i3i3−i3i32-2-11−i3i3−i3i3-1-1-111002200-2-2−i3i3−i3i3-1-1-1-100i3−i3i3−i31111-11−i3i3−i3i30000000000000000
χ5022-2-2-22-2-12-22-122-2-21100001-11−i3i3−i3i32-2-11−i3i3−i3i3-1-1-11100-2-20022i3−i3i3−i3111100−i3i3−i3i3-1-1-1-1-11−i3i3−i3i30000000000000000
χ5122-2-2-22-2-12-22-122-2-21100001-11i3−i3i3−i32-2-11i3−i3i3−i3-1-1-111002200-2-2i3−i3i3−i3-1-1-1-100−i3i3−i3i31111-11i3−i3i3−i30000000000000000
χ5222-2-2-22-2-12-22-122-2-21100001-11i3−i3i3−i32-2-11i3−i3i3−i3-1-1-11100-2-20022−i3i3−i3i3111100i3−i3i3−i3-1-1-1-1-11i3−i3i3−i30000000000000000
χ5322-2-2-22-2-12-22-1-2-2221100001-11−i3i3−i3i3-22-11−i3i3−i3i3-111-1-1002-200-22−i3i3i3−i3-1-11100i3−i3−i3i311-1-11-1i3−i3i3−i30000000000000000
χ5422-2-2-22-2-12-22-1-2-2221100001-11−i3i3−i3i3-22-11−i3i3−i3i3-111-1-100-22002-2i3−i3−i3i311-1-100−i3i3i3−i3-1-1111-1i3−i3i3−i30000000000000000
χ5522-2-2-22-2-12-22-1-2-2221100001-11i3−i3i3−i3-22-11i3−i3i3−i3-111-1-1002-200-22i3−i3−i3i3-1-11100−i3i3i3−i311-1-11-1−i3i3−i3i30000000000000000
χ5622-2-2-22-2-12-22-1-2-2221100001-11i3−i3i3−i3-22-11i3−i3i3−i3-111-1-100-22002-2−i3i3i3−i311-1-100i3−i3−i3i3-1-1111-1−i3i3−i3i30000000000000000
χ5722-2-2-2-222-222222-2-2-2-20000-2-220000-22-220000222-2-22200-2-2002222000000-2-2-2-20000-2200000000000000000000
χ5822-2-2-2-222-222222-2-2-2-20000-2-220000-22-220000222-2-2-2-2002200-2-2-2-200000022220000-2200000000000000000000
χ5922-2-2-2-222-2222-2-222-2-20000-2-2200002-2-2200002-2-2222-200-220022-2-2000000-2-22200002-200000000000000000000
χ6022-2-2-2-222-2222-2-222-2-20000-2-2200002-2-2200002-2-222-22002-200-2-22200000022-2-200002-200000000000000000000
χ6122-2-2-2-22-1-222-122-2-211000011-1−i3i3i3−i3-221-1−i3i3i3−i3-1-1-1112200-2-200-1-1-1-1−i3i3−i3i3001111i3−i3i3−i31-1−i3i3i3−i30000000000000000
χ6222-2-2-2-22-1-222-122-2-211000011-1−i3i3i3−i3-221-1−i3i3i3−i3-1-1-111-2-20022001111i3−i3i3−i300-1-1-1-1−i3i3−i3i31-1−i3i3i3−i30000000000000000
χ6322-2-2-2-22-1-222-122-2-211000011-1i3−i3−i3i3-221-1i3−i3−i3i3-1-1-1112200-2-200-1-1-1-1i3−i3i3−i3001111−i3i3−i3i31-1i3−i3−i3i30000000000000000
χ6422-2-2-2-22-1-222-122-2-211000011-1i3−i3−i3i3-221-1i3−i3−i3i3-1-1-111-2-20022001111−i3i3−i3i300-1-1-1-1i3−i3i3−i31-1i3−i3−i3i30000000000000000
χ6522-2-2-2-22-1-222-1-2-22211000011-1−i3i3i3−i32-21-1−i3i3i3−i3-111-1-12-200-2200-1-111−i3i3i3−i30011-1-1i3−i3−i3i3-11i3−i3−i3i30000000000000000
χ6622-2-2-2-22-1-222-1-2-22211000011-1−i3i3i3−i32-21-1−i3i3i3−i3-111-1-1-22002-20011-1-1i3−i3−i3i300-1-111−i3i3i3−i3-11i3−i3−i3i30000000000000000
χ6722-2-2-2-22-1-222-1-2-22211000011-1i3−i3−i3i32-21-1i3−i3−i3i3-111-1-12-200-2200-1-111i3−i3−i3i30011-1-1−i3i3i3−i3-11−i3i3i3−i30000000000000000
χ6822-2-2-2-22-1-222-1-2-22211000011-1i3−i3−i3i32-21-1i3−i3−i3i3-111-1-1-22002-20011-1-1−i3i3i3−i300-1-111i3−i3−i3i3-11−i3i3i3−i30000000000000000
χ694444-44-44-44-440000440000-44-4000000-440000-40000000000000000000000000000000000000000000000000000
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χ7544-4-4444-2-4-4-4-20000224-4-44-2-2-2-2-222002222-2-220000000000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-2000022-444-4-2-2-222-2-20022-2-22220000000000000000000000000000000000000000000000000000
χ7744-4-44-4-4-244-4-200002244-4-4-222-2-2-2-200-2-2222220000000000000000000000000000000000000000000000000000
χ7844-4-44-4-4-244-4-2000022-4-444-222222200-2-2-2-2-2-220000000000000000000000000000000000000000000000000000
χ794-44i−4i0004000-422−22−2i22i24i−4i0000000000000000000022−22−2i22i2000000000000000000000000000000002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ804-44i−4i0004000-422−22−2i22i24i−4i0000000000000000000022−22−2i22i200000000000000000000000000000000-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ814-44i−4i0004000-4−22222i2−2i24i−4i00000000000000000000−22222i2−2i2000000000000000000000000000000002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ824-44i−4i0004000-4−22222i2−2i24i−4i00000000000000000000−22222i2−2i200000000000000000000000000000000-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ834-4−4i4i0004000-422−222i2−2i2−4i4i0000000000000000000022−222i2−2i2000000000000000000000000000000002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ844-4−4i4i0004000-422−222i2−2i2−4i4i0000000000000000000022−222i2−2i200000000000000000000000000000000-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ854-4−4i4i0004000-4−2222−2i22i2−4i4i00000000000000000000−2222−2i22i2000000000000000000000000000000002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ864-4−4i4i0004000-4−2222−2i22i2−4i4i00000000000000000000−2222−2i22i200000000000000000000000000000000-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ878-88i−8i000-4000442−42−4i24i2−4i4i00000000000000000000−22222i2−2i2000000000000000000000000000000000000000000000000
χ888-88i−8i000-40004−42424i2−4i2−4i4i0000000000000000000022−22−2i22i2000000000000000000000000000000000000000000000000
χ898-8−8i8i000-4000442−424i2−4i24i−4i00000000000000000000−2222−2i22i2000000000000000000000000000000000000000000000000
χ908-8−8i8i000-40004−4242−4i24i24i−4i0000000000000000000022−222i2−2i2000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.