Finite Group Databasebeta

← Group #10692430

Character table — Group #10692430

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888121212121616161616161616161624242424242448484848
order122234444666244446612121212121212122244888812122424242424242424888866881212242424248888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1
χ911111-1-1-1-1111-111-11-1-111-1-1-1-1-1-11-11-1ii−i−i11iiii−i−i−i−iii−i−i1-1i−i1-1ii−i−ii−iii−i−i1-11-1
χ1011111-1-1-1-1111-111-11-1-111-1-1-1-1-1-11-11-1ii−i−i11iiii−i−i−i−i−i−iii1-1i−i1-1ii−i−i−ii−i−iii-11-11
χ1111111-1-1-1-1111-111-11-1-111-1-1-1-1-1-11-11-1−i−iii11−i−i−i−iiiiiii−i−i1-1−ii1-1−i−iiii−iii−i−i-11-11
χ1211111-1-1-1-1111-111-11-1-111-1-1-1-1-1-11-11-1−i−iii11−i−i−i−iiiii−i−iii1-1−ii1-1−i−iii−ii−i−iii1-11-1
χ1311111-1-1-1-1111-111-11-1-111-1-1-1-1-1-1-11-11ii−i−i11iiii−i−i−i−iii−i−i-11−ii-11−i−iiii−i−i−iii1-1-11
χ1411111-1-1-1-1111-111-11-1-111-1-1-1-1-1-1-11-11ii−i−i11iiii−i−i−i−i−i−iii-11−ii-11−i−iii−iiii−i−i-111-1
χ1511111-1-1-1-1111-111-11-1-111-1-1-1-1-1-1-11-11−i−iii11−i−i−i−iiiiiii−i−i-11i−i-11ii−i−ii−i−i−iii-111-1
χ1611111-1-1-1-1111-111-11-1-111-1-1-1-1-1-1-11-11−i−iii11−i−i−i−iiiii−i−iii-11i−i-11ii−i−i−iiii−i−i1-1-11
χ17222222222222-2-22-2-2-2-2-2-2222-2-22000000002-20000000022220000000000-2-200000000
χ18222222222222-2-22-2-2-2-2-2-2222-2-22000000002-200000000-2-2-2-200000000002200000000
χ192222222-2-222222-2-2-222222-2-2-2-2200000000-2-20000000000000000000000002i−2i2i−2i0000
χ202222222-2-222222-2-2-222222-2-2-2-2200000000-2-2000000000000000000000000−2i2i−2i2i0000
χ212222222-2-2222-2-2-222-2-2-2-22-2-222222-2-20000-220000000000002200-2-200000000000000
χ222222222-2-2222-2-2-222-2-2-2-22-2-2222-2-2220000-22000000000000-2-2002200000000000000
χ2322222-2-2222222-2-2-2222-2-2-222-2-2-22-2-220000-220000000000002-200-2200000000000000
χ2422222-2-2222222-2-2-2222-2-2-222-2-2-2-222-20000-22000000000000-22002-200000000000000
χ2522222-2-222222-22-22-2-2-222-22222-200000000-2-20000000000000000000000002-2-220000
χ2622222-2-222222-22-22-2-2-222-22222-200000000-2-2000000000000000000000000-222-20000
χ2722222-2-2-2-22222-222-222-2-2-2-2-222-2000000002-2000000002i2i−2i−2i0000000000−2i2i00000000
χ2822222-2-2-2-22222-222-222-2-2-2-2-222-2000000002-200000000−2i−2i2i2i00000000002i−2i00000000
χ292222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000-1-122-1-1-1-1-1-10000000000
χ302222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-1-1-2-2-1-111110000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000011-2-21111110000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000112211-1-1-1-10000000000
χ332222-122-2-2-1-1-1-2-2-2221111-111-1-1-122-2-200001-1−i3−i3i3i3−i3−i3i3i30000-1-10011−i3i3−i3i30000000000
χ342222-122-2-2-1-1-1-2-2-2221111-111-1-1-122-2-200001-1i3i3−i3−i3i3i3−i3−i30000-1-10011i3−i3i3−i30000000000
χ352222-122-2-2-1-1-1-2-2-2221111-111-1-1-1-2-22200001-1−i3−i3i3i3−i3−i3i3i300001100-1-1i3−i3i3−i30000000000
χ362222-122-2-2-1-1-1-2-2-2221111-111-1-1-1-2-22200001-1i3i3−i3−i3i3i3−i3−i300001100-1-1−i3i3−i3i30000000000
χ372222-1-2-222-1-1-12-2-2-22-1-1111-1-11112-2-2200001-133−3−3−3−3330000-11001-13−3−330000000000
χ382222-1-2-222-1-1-12-2-2-22-1-1111-1-11112-2-2200001-1−3−33333−3−30000-11001-1−333−30000000000
χ392222-1-2-222-1-1-12-2-2-22-1-1111-1-1111-222-200001-133−3−3−3−33300001-100-11−333−30000000000
χ402222-1-2-222-1-1-12-2-2-22-1-1111-1-1111-222-200001-1−3−33333−3−300001-100-113−3−330000000000
χ412222-1-2-2-2-2-1-1-1-222-2211-1-11111112-22-22i2i−2i−2i-1-1−i−i−i−iiiii0000-112i−2i-11−i−iii0000000000
χ422222-1-2-2-2-2-1-1-1-222-2211-1-11111112-22-2−2i−2i2i2i-1-1iiii−i−i−i−i0000-11−2i2i-11ii−i−i0000000000
χ432222-1-2-2-2-2-1-1-1-222-2211-1-1111111-22-222i2i−2i−2i-1-1−i−i−i−iiiii00001-1−2i2i1-1ii−i−i0000000000
χ442222-1-2-2-2-2-1-1-1-222-2211-1-1111111-22-22−2i−2i2i2i-1-1iiii−i−i−i−i00001-12i−2i1-1−i−iii0000000000
χ454444-24444-2-2-2-4-44-4-42222-2-2-222-200000000-2200000000000000000000000000000000
χ464444-244-4-4-2-2-244-4-4-4-2-2-2-2-22222-2000000002200000000000000000000000000000000
χ474444-2-4-444-2-2-2-44-44-422-2-22-2-2-2-22000000002200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-24-444-4-2-222222-2-2200000000-2200000000000000000000000000000000
χ4944-4-444-4004-4-400000000040000-400000000000000000022−2222−2200000000000000000000
χ5044-4-444-4004-4-400000000040000-4000000000000000000−2222−222200000000000000000000
χ5144-4-44-44004-4-4000000000-400004000000000000000000−2i22i22i2−2i200000000000000000000
χ5244-4-44-44004-4-4000000000-4000040000000000000000002i2−2i2−2i22i200000000000000000000
χ534-44-44004i−4i-44-400000000004i−4i00000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ544-44-44004i−4i-44-400000000004i−4i0000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ554-44-4400−4i4i-44-40000000000−4i4i0000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000
χ564-44-4400−4i4i-44-40000000000−4i4i00000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000
χ574-44-4-2004i−4i2-22000000023−230−2i2i−2i32i3000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23000000000000000000000000
χ584-44-4-2004i−4i2-22000000023−230−2i2i−2i32i300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23000000000000000000000000
χ594-44-4-2004i−4i2-220000000−23230−2i2i2i3−2i3000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23000000000000000000000000
χ604-44-4-2004i−4i2-220000000−23230−2i2i2i3−2i300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23000000000000000000000000
χ614-44-4-200−4i4i2-22000000023−2302i−2i2i3−2i300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23000000000000000000000000
χ624-44-4-200−4i4i2-22000000023−2302i−2i2i3−2i3000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23000000000000000000000000
χ634-44-4-200−4i4i2-220000000−232302i−2i−2i32i300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23000000000000000000000000
χ644-44-4-200−4i4i2-220000000−232302i−2i−2i32i3000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23000000000000000000000000
χ6588-8-8-48-800-444000000000-400004000000000000000000000000000000000000000000
χ6688-8-8-4-8800-44400000000040000-4000000000000000000000000000000000000000000
χ678-8-8880000-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-88-4000044-400000−4i34i300000000000000000000000000000000000000000000000000
χ698-8-88-4000044-4000004i3−4i300000000000000000000000000000000000000000000000000

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