Finite Group Databasebeta

← Group #10695812

Character table — Group #10695812

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order122222344446662244661212121212121212668888242424242424242488882424242424242424444488882444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-11-1
χ922222222222222-2-2-2-2222222-2-2-2-2-2-222-2-22222-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000
χ112222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-22200000000000000000000000000002i2i−2i−2i0000
χ122222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-2220000000000000000000000000000−2i−2i2i2i0000
χ132222222-2-2-2-2222-2-22222-2-2-2-22222-2-200000000000000000000000022-2-200000000
χ142222222-2-2-2-2222-2-22222-2-2-2-22222-2-2000000000000000000000000-2-22200000000
χ15222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2221111-1-1-1-1000000000000
χ19222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-11111000033−3−333−3−3000000000000
χ20222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-111111122-2-2-1-1-1-111110000−3−333−3−333000000000000
χ21222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1111111-2-2221111-1-1-1-1000033−3−3−3−333000000000000
χ22222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1111111-2-2221111-1-1-1-10000−3−33333−3−3000000000000
χ232222-2-2222-2-22222-22-2-2-2-2-22222-2-22-20000000000000000000000000000000020-20
χ242222-2-2222-2-22222-22-2-2-2-2-22222-2-22-200000000000000000000000000000000-2020
χ252222-2-2222-2-2222-22-22-2-2-2-222-2-222-2200000000000000000000000000000000020-2
χ262222-2-2222-2-2222-22-22-2-2-2-222-2-222-22000000000000000000000000000000000-202
χ272222-2-22-2-2222222-2-22-2-222-2-2-2-2222-2000000000000002-200002-22-2000000000000
χ282222-2-22-2-2222222-2-22-2-222-2-2-2-2222-200000000000000-220000-22-22000000000000
χ292222-2-22-2-222222-222-2-2-222-2-222-2-2-220000000000002-2002-22-20000000000000000
χ302222-2-22-2-222222-222-2-2-222-2-222-2-2-22000000000000-2200-22-220000000000000000
χ312222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-1-11000033−3−333−3−3002-23−3−33-11-11000000000000
χ322222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-1-11000033−3−333−3−300-22−333−31-11-1000000000000
χ332222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-1-110000−3−333−3−333002-2−333−3-11-11000000000000
χ342222-2-2-1-2-222-1-1-12-2-2211-1-11111-1-1-110000−3−333−3−33300-223−3−331-11-1000000000000
χ352222-2-2-1-2-222-1-1-1-222-211-1-111-1-1111-1000033−3−3−3−3332-200-11-11−333−3000000000000
χ362222-2-2-1-2-222-1-1-1-222-211-1-111-1-1111-1000033−3−3−3−333-22001-11-13−3−33000000000000
χ372222-2-2-1-2-222-1-1-1-222-211-1-111-1-1111-10000−3−33333−3−32-200-11-113−3−33000000000000
χ382222-2-2-1-2-222-1-1-1-222-211-1-111-1-1111-10000−3−33333−3−3-22001-11-1−333−3000000000000
χ39444444-2-4-4-4-4-2-2-244-4-4-2-222222222-2-2000000000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-2-4-444-2-22222-2-2-2-222000000000000000000000000000000000000
χ414444-4-4-244-4-4-2-2-24-44-42222-2-2-2-222-22000000000000000000000000000000000000
χ424444-4-4-244-4-4-2-2-2-44-442222-2-222-2-22-2000000000000000000000000000000000000
χ4344-4-40044-400-4-44000000004-40000000000000000000000000000002i−2i2i−2i00000000
χ4444-4-40044-400-4-44000000004-4000000000000000000000000000000−2i2i−2i2i00000000
χ4544-4-4004-4400-4-4400000000-440000000000000000000000000000002i−2i−2i2i00000000
χ4644-4-4004-4400-4-4400000000-44000000000000000000000000000000−2i2i2i−2i00000000
χ474-44-4004004i−4i4-4-40000004i−4i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ484-44-4004004i−4i4-4-40000004i−4i000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ494-44-400400−4i4i4-4-4000000−4i4i000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ504-44-400400−4i4i4-4-4000000−4i4i0000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ514-4-444-440000-44-400004-4000000000000−2i22i20000−2i22i2−2i22i2000000000000000000000000
χ524-4-444-440000-44-400004-40000000000002i2−2i200002i2−2i22i2−2i2000000000000000000000000
χ534-4-444-4-200002-220000-22000023−2323−230000−2i22i2i6−i6i6−i6i2−i2i2−i2000000000000000000000000
χ544-4-444-4-200002-220000-22000023−2323−2300002i2−2i2−i6i6−i6i6−i2i2−i2i2000000000000000000000000
χ554-4-444-4-200002-220000-220000−2323−23230000−2i22i2−i6i6−i6i6i2−i2i2−i2000000000000000000000000
χ564-4-444-4-200002-220000-220000−2323−232300002i2−2i2i6−i6i6−i6−i2i2−i2i2000000000000000000000000
χ574-4-44-4440000-44-40000-440000000000−2i22i200−2i22i22i2−2i20000000000000000000000000000
χ584-4-44-4440000-44-40000-4400000000002i2−2i2002i2−2i2−2i22i20000000000000000000000000000
χ594-4-44-44-200002-2200002-2000023−23−232300−2i22i200i2−i2−i2i2i6−i6−i6i6000000000000000000000000
χ604-4-44-44-200002-2200002-2000023−23−2323002i2−2i200−i2i2i2−i2−i6i6i6−i6000000000000000000000000
χ614-4-44-44-200002-2200002-20000−232323−2300−2i22i200i2−i2−i2i2−i6i6i6−i6000000000000000000000000
χ624-4-44-44-200002-2200002-20000−232323−23002i2−2i200−i2i2i2−i2i6−i6−i6i6000000000000000000000000
χ6388-8-800-48-80044-400000000-44000000000000000000000000000000000000000000
χ6488-8-800-4-880044-4000000004-4000000000000000000000000000000000000000000
χ658-88-800-4008i−8i-444000000−4i4i00000000000000000000000000000000000000000000
χ668-88-800-400−8i8i-4440000004i−4i00000000000000000000000000000000000000000000

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