Finite Group Databasebeta

← Group #10691872

Character table — Group #10691872

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1222223444466612121212444466888812122424242424242424224466668888881212121212121212242424242424242424242424888888882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1111-1-1111-1-1-1-11-11-1-1-1ii−i−i11iiii−i−i−i−i11-1-11111i−iii−i−i11-1-1-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1111-1-1111-1-1-1-11-11-1-1-1ii−i−i11iiii−i−i−i−i11-1-11111i−iii−i−i11-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1111-1-1111-1-1-1-11-11-1-1-1ii−i−i11iiii−i−i−i−i-1-111-1-1-1-1i−i−i−iii11-1-11111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1111-1-1111-1-1-1-11-11-1-1-1ii−i−i11iiii−i−i−i−i-1-111-1-1-1-1i−i−i−iii11-1-11111ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1111-1-1111-1-1-1-11-11-1-1-1−i−iii11−i−i−i−iiiii11-1-11111−ii−i−iii11-1-1-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1111-1-1111-1-1-1-11-11-1-1-1−i−iii11−i−i−i−iiiii11-1-11111−ii−i−iii11-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1111-1-1111-1-1-1-11-11-1-1-1−i−iii11−i−i−i−iiiii-1-111-1-1-1-1−iiii−i−i11-1-11111−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1111-1-1111-1-1-1-11-11-1-1-1−i−iii11−i−i−i−iiiii-1-111-1-1-1-1−iiii−i−i11-1-11111−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222-2-2-2-2222222222222222200000000-2-20000-2-2-2-20000-2-2-2-200000000000000000000
χ18222222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-200000000220000-2-2-2-20000222200000000000000000000
χ192222222-2-2-2-2222-2-2-2-222-2-2220000-2-20000000000000000002i−2i2i−2i2-22-2000000002i2i−2i−2i2i2i−2i−2i000000000000
χ202222222-2-2-2-2222-2-2-2-222-2-2220000-2-2000000000000000000−2i2i−2i2i2-22-200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ212222222-2-2-2-2222-2-2-2-2-2-222220000-2-2000000002-22-222-2-2000000-22-2222-2-2000000000000000000000000
χ222222222-2-2-2-2222-2-2-2-2-2-222220000-2-200000000-22-22-2-222000000-22-22-2-222000000000000000000000000
χ23222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111122-2-2-2-2-1-1-1-11111-1-1-1-111111111000000000000
χ25222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1111111112222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111000000000000
χ26222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-111111111-2-2-2-21111-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000−i3i3−i3i3-2-200001111−i3i3−i3i31111−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000i3−i3i3−i3-2-200001111i3−i3i3−i31111i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-1111111110000−i3i3−i3i32200001111−i3i3−i3i3-1-1-1-1i3−i3i3−i3i3−i3i3−i3000000000000
χ30222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-1111111110000i3−i3i3−i32200001111i3−i3i3−i3-1-1-1-1−i3i3−i3i3−i3i3−i3i3000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-2-1-100001133−3−333−3−30000−i3i3i3−i3002i−2i2i−2i-11-11−i3i3i3−i33−33−3−i−iii−i−iii000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-2-1-100001133−3−333−3−30000i3−i3−i3i300−2i2i−2i2i-11-11i3−i3−i3i33−33−3ii−i−iii−i−i000000000000
χ33222222-1-2-2-2-2-1-1-1111122-2-2-1-1000011−3−333−3−3330000−i3i3i3−i300−2i2i−2i2i-11-11−i3i3i3−i3−33−33ii−i−iii−i−i000000000000
χ34222222-1-2-2-2-2-1-1-1111122-2-2-1-1000011−3−333−3−3330000i3−i3−i3i3002i−2i2i−2i-11-11i3−i3−i3i3−33−33−i−iii−i−iii000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-222-1-100001133−3−333−3−32-22-2-1-1110000001-11-1-1-111−33−333−3−333−3−33000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-222-1-100001133−3−333−3−3-22-2211-1-10000001-11-111-1-1−33−33−333−3−333−3000000000000
χ37222222-1-2-2-2-2-1-1-11111-2-222-1-1000011−3−333−3−3332-22-2-1-1110000001-11-1-1-1113−33−3−333−3−333−3000000000000
χ38222222-1-2-2-2-2-1-1-11111-2-222-1-1000011−3−333−3−333-22-2211-1-10000001-11-111-1-13−33−33−3−333−3−33000000000000
χ392222-2-2222-2-2222-2-2-2-2-22-22-2-22i2i−2i−2i222i2i2i2i−2i−2i−2i−2i00000000−2i2i0000-2-2220000−2i−2i2i2i00000000000000000000
χ402222-2-2222-2-2222-2-2-2-2-22-22-2-2−2i−2i2i2i22−2i−2i−2i−2i2i2i2i2i000000002i−2i0000-2-22200002i2i−2i−2i00000000000000000000
χ412222-2-22-2-22222222222-2-22-2-20000-2-20000000000000000002-2-222-2-220000000022-2-2-2-222000000000000
χ422222-2-22-2-22222222222-2-22-2-20000-2-2000000000000000000-222-22-2-2200000000-2-22222-2-2000000000000
χ432222-2-22-2-2222222222-222-2-2-20000-2-2000000002-2-2222-2-2000000-222-2-2-222000000000000000000000000
χ442222-2-22-2-2222222222-222-2-2-20000-2-200000000-222-2-2-222000000-222-222-2-2000000000000000000000000
χ452222-2-2-122-2-2-1-1-111112-22-2112i2i−2i−2i-1-1−i−i−i−iiiii22-2-2-1-1-1-12i−2i2i2i−2i−2i-1-1111111−i−iii−i−i−i−iiiii000000000000
χ462222-2-2-122-2-2-1-1-111112-22-2112i2i−2i−2i-1-1−i−i−i−iiiii-2-22211112i−2i−2i−2i2i2i-1-111-1-1-1-1−i−iiiiiii−i−i−i−i000000000000
χ472222-2-2-122-2-2-1-1-111112-22-211−2i−2i2i2i-1-1iiii−i−i−i−i22-2-2-1-1-1-1−2i2i−2i−2i2i2i-1-1111111ii−i−iiiii−i−i−i−i000000000000
χ482222-2-2-122-2-2-1-1-111112-22-211−2i−2i2i2i-1-1iiii−i−i−i−i-2-2221111−2i2i2i2i−2i−2i-1-111-1-1-1-1ii−i−i−i−i−i−iiiii000000000000
χ492222-2-2-122-2-2-1-1-11111-22-22112i2i−2i−2i-1-1−i−i−i−iiiii0000−i3i3−i3i3−2i2i000011-1-1i3−i3i3−i3ii−i−i3−33−3−33−33000000000000
χ502222-2-2-122-2-2-1-1-11111-22-22112i2i−2i−2i-1-1−i−i−i−iiiii0000i3−i3i3−i3−2i2i000011-1-1−i3i3−i3i3ii−i−i−33−333−33−3000000000000
χ512222-2-2-122-2-2-1-1-11111-22-2211−2i−2i2i2i-1-1iiii−i−i−i−i0000−i3i3−i3i32i−2i000011-1-1i3−i3i3−i3−i−iii−33−333−33−3000000000000
χ522222-2-2-122-2-2-1-1-11111-22-2211−2i−2i2i2i-1-1iiii−i−i−i−i0000i3−i3i3−i32i−2i000011-1-1−i3i3−i3i3−i−iii3−33−3−33−33000000000000
χ532222-2-2-1-2-222-1-1-1-1-1-1-12-2-2211000011−i3−i3i3i3i3i3−i3−i30000−i3i3i3−i3002-2-22-111-1i3−i3−i3i3−i3i3i3−i3-1-11111-1-1000000000000
χ542222-2-2-1-2-222-1-1-1-1-1-1-12-2-2211000011−i3−i3i3i3i3i3−i3−i30000i3−i3−i3i300-222-2-111-1−i3i3i3−i3−i3i3i3−i311-1-1-1-111000000000000
χ552222-2-2-1-2-222-1-1-1-1-1-1-12-2-2211000011i3i3−i3−i3−i3−i3i3i30000−i3i3i3−i300-222-2-111-1i3−i3−i3i3i3−i3−i3i311-1-1-1-111000000000000
χ562222-2-2-1-2-222-1-1-1-1-1-1-12-2-2211000011i3i3−i3−i3−i3−i3i3i30000i3−i3−i3i3002-2-22-111-1−i3i3i3−i3i3−i3−i3i3-1-11111-1-1000000000000
χ572222-2-2-1-2-222-1-1-1-1-1-1-1-222-211000011−i3−i3i3i3i3i3−i3−i32-2-22-1-1110000001-1-1111-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000
χ582222-2-2-1-2-222-1-1-1-1-1-1-1-222-211000011−i3−i3i3i3i3i3−i3−i3-222-211-1-10000001-1-11-1-111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000
χ592222-2-2-1-2-222-1-1-1-1-1-1-1-222-211000011i3i3−i3−i3−i3−i3i3i32-2-22-1-1110000001-1-1111-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000
χ602222-2-2-1-2-222-1-1-1-1-1-1-1-222-211000011i3i3−i3−i3−i3−i3i3i3-222-211-1-10000001-1-11-1-111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000
χ612-2-222-222-22-2-2-2222-2-200002-22i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002−22−2−i2i2−i2i20000
χ622-2-222-222-22-2-2-2222-2-200002-22i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−22−22i2−i2i2−i20000
χ632-2-222-222-22-2-2-2222-2-200002-2−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002−22−2i2−i2i2−i20000
χ642-2-222-222-22-2-2-2222-2-200002-2−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−22−22−i2i2−i2i20000
χ652-2-22-2222-2-22-2-22-2-2220000-222-2-222-22-22-2-22-2200000000000000000000000000000000002−2−22−222−20000
χ662-2-22-2222-2-22-2-22-2-2220000-222-2-222-22-22-2-22-220000000000000000000000000000000000−222−22−2−220000
χ672-2-22-2222-2-22-2-22-2-2220000-22-222-22-2-22-222-22-200000000000000000000000000000000002−2−222−2−220000
χ682-2-22-2222-2-22-2-22-2-2220000-22-222-22-2-22-222-22-20000000000000000000000000000000000−222−2−222−20000
χ694-4-444-44-44-44-4-44-4-44400004-40000-44000000000000000000000000000000000000000000000000000000
χ704-4-444-4-24-44-422-2-2-2220000-224i−4i4i−4i-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ714-4-444-4-24-44-422-2-2-2220000-22−4i4i−4i4i-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ724-4-444-4-2-44-4422-222-2-20000-2200002-2−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ734-4-444-4-2-44-4422-222-2-20000-2200002-22i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ744-4-44-444-444-4-4-4444-4-40000-440000-44000000000000000000000000000000000000000000000000000000
χ754-4-44-44-24-4-4422-222-2-200002-24-4-44-22-22-222-22-20000000000000000000000000000000000000000000000
χ764-4-44-44-24-4-4422-222-2-200002-2-444-4-222-22-2-22-220000000000000000000000000000000000000000000000
χ774-4-44-44-2-444-422-2-2-22200002-200002-223−23−2323−232323−230000000000000000000000000000000000000000000000
χ784-4-44-44-2-444-422-2-2-22200002-200002-2−232323−2323−23−23230000000000000000000000000000000000000000000000
χ7988-8-800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-40000-44443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-40000-444−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-800-400004-4443−43−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-400004-44−434343−43000000000000000000000000000000000000000000000000000000000000000000

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