Finite Group Databasebeta

← Group #10691312

Character table — Group #10691312

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122244443444444446661212121212121212121212122466888888881212121212122424242424242424242424242424242424446688881212121212122424242424242424888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111ii−i−i11-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111ii−i−i11-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1−i−iii-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1−i−iii-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111−i−iii11-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111−i−iii11-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1ii−i−i-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1-1-1111-1-111-1-11111111-1-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1ii−i−i-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ172222222222222-2-2-2-2222222222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2222222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-22200000000000000002-2-22220000-2-222-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-2220000000000000000-222-2-2-2000022-2-22200000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-2222200000000-2-222-2-200000000000000000000002i−2i2i−2i0000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-2222200000000-2-222-2-20000000000000000000000−2i2i−2i2i000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-211111111111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111112222-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-2112222111111-1-1-1-1-1-1-1-1000000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-2-222-2-2111111-1-1-1-11111-1-1-1-111110000−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21122-2-222-2-2111111-1-1-1-11111-1-1-1-111110000i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ2922222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-222-2-2221111111111-1-1-1-11111-1-1-1-10000−i3i30000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000
χ3022222222-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-222-2-2221111111111-1-1-1-11111-1-1-1-10000i3−i30000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000
χ3122222222-1-2-2-2-22222-1-1-11111-1-1-1-11111-2-21100000000-1-111-1-133−3−333−3−333−3−333−3−32-2-22-1-1000011-1-1113−3−333−3−33000000000000
χ3222222222-1-2-2-2-22222-1-1-11111-1-1-1-11111-2-21100000000-1-111-1-133−3−333−3−333−3−333−3−3-222-2110000-1-111-1-1−333−3−333−3000000000000
χ3322222222-1-2-2-2-22222-1-1-11111-1-1-1-11111-2-21100000000-1-111-1-1−3−333−3−333−3−333−3−3332-2-22-1-1000011-1-111−333−3−333−3000000000000
χ3422222222-1-2-2-2-22222-1-1-11111-1-1-1-11111-2-21100000000-1-111-1-1−3−333−3−333−3−333−3−333-222-2110000-1-111-1-13−3−333−3−33000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1111122-1-10000000011-1-11133−3−3−3−33333−3−3−3−3330000−i3i32i−2i2i−2ii3−i3−i3i3i3−i3−i−iii−i−iii000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1111122-1-10000000011-1-11133−3−3−3−33333−3−3−3−3330000i3−i3−2i2i−2i2i−i3i3i3−i3−i3i3ii−i−iii−i−i000000000000
χ3722222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1111122-1-10000000011-1-111−3−33333−3−3−3−33333−3−30000−i3i3−2i2i−2i2ii3−i3−i3i3i3−i3ii−i−iii−i−i000000000000
χ3822222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1111122-1-10000000011-1-111−3−33333−3−3−3−33333−3−30000i3−i32i−2i2i−2i−i3i3i3−i3−i3i3−i−iii−i−iii000000000000
χ392222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-2222i2i−2i−2i−2i−2i2i2i-2-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ402222-2-2-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-22-222−2i−2i2i2i2i2i−2i−2i-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ412222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-222222-2220000000022-2-2-2-200000000000000002-22-2220000-2-2-2-22200000000000000000000
χ422222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-222222-2220000000022-2-2-2-20000000000000000-22-22-2-200002222-2-200000000000000000000
χ432222-2-2-2-22-2-222-2-222222-2-2-2-2-2-2-2-22222-22-2-200000000-2-2222200000000000000000000002-2-2200000022-2-2-2-222000000000000
χ442222-2-2-2-22-2-222-2-222222-2-2-2-2-2-2-2-22222-22-2-200000000-2-222220000000000000000000000-222-2000000-2-22222-2-2000000000000
χ452222-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-22112i2i2i2i−2i−2i−2i−2i-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-2-1-12i2i−2i−2i-1-11111−i−i−i−iiiii000000000000
χ462222-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-22112i2i2i2i−2i−2i−2i−2i-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-2-22211−2i−2i2i2i11-1-1-1-1iiii−i−i−i−i000000000000
χ472222-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-2211−2i−2i−2i−2i2i2i2i2i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i22-2-2-1-1−2i−2i2i2i-1-11111iiii−i−i−i−i000000000000
χ482222-2-2-2-2-122-2-222-2-2-1-1-1-1-1-1-111111111-2211−2i−2i−2i−2i2i2i2i2i-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-2-222112i2i−2i−2i11-1-1-1-1−i−i−i−iiiii000000000000
χ492222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112-2-1-12i2i−2i−2i−2i−2i2i2i1111-1-1−i−i−i−iiiiiiiii−i−i−i−i0000−i3i30000−i3i3i3−i3i3−i33−33−3−33−33000000000000
χ502222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112-2-1-12i2i−2i−2i−2i−2i2i2i1111-1-1−i−i−i−iiiiiiiii−i−i−i−i0000i3−i30000i3−i3−i3i3−i3i3−33−333−33−3000000000000
χ512222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112-2-1-1−2i−2i2i2i2i2i−2i−2i1111-1-1iiii−i−i−i−i−i−i−i−iiiii0000−i3i30000−i3i3i3−i3i3−i3−33−333−33−3000000000000
χ522222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112-2-1-1−2i−2i2i2i2i2i−2i−2i1111-1-1iiii−i−i−i−i−i−i−i−iiiii0000i3−i30000i3−i3−i3i3−i3i33−33−3−33−33000000000000
χ532222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-100000000-1-11111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-22-2-1-100001111-1-1−i3i3i3−i3i3−i3−i3i3000000000000
χ542222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-100000000-1-11111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-22-22110000-1-1-1-111i3−i3−i3i3−i3i3i3−i3000000000000
χ552222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-100000000-1-11111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i32-22-2-1-100001111-1-1i3−i3−i3i3−i3i3i3−i3000000000000
χ562222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-12-2-1-100000000-1-11111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-22-22110000-1-1-1-111−i3i3i3−i3i3−i3−i3i3000000000000
χ572222-2-2-2-2-1-2-222-2-222-1-1-111111111-1-1-1-1-22110000000011-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−i3i32-2-22i3−i3i3−i3−i3i3-1-11111-1-1000000000000
χ582222-2-2-2-2-1-2-222-2-222-1-1-111111111-1-1-1-1-22110000000011-1-1-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000i3−i3-222-2−i3i3−i3i3i3−i311-1-1-1-111000000000000
χ592222-2-2-2-2-1-2-222-2-222-1-1-111111111-1-1-1-1-22110000000011-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000−i3i3-222-2i3−i3i3−i3−i3i311-1-1-1-111000000000000
χ602222-2-2-2-2-1-2-222-2-222-1-1-111111111-1-1-1-1-22110000000011-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000i3−i32-2-22−i3i3−i3i3i3−i3-1-11111-1-1000000000000
χ6122-2-22i−2i2i−2i22-22i−2i00002-2-222-2-22i2i−2i−2i2i2i−2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000002−2−i2i21−i−1+i1+i−1−i0000
χ6222-2-22i−2i2i−2i22-22i−2i00002-2-222-2-22i2i−2i−2i2i2i−2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000−22i2−i2−1+i1−i−1−i1+i0000
χ6322-2-22i−2i2i−2i22-22i−2i00002-2-222-2-22i2i−2i−2i2i2i−2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000002−2−i2i2−1+i1−i−1−i1+i0000
χ6422-2-22i−2i2i−2i22-22i−2i00002-2-222-2-22i2i−2i−2i2i2i−2i−2i0000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000−22i2−i21−i−1+i1+i−1−i0000
χ6522-2-2−2i2i−2i2i22-2−2i2i00002-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000002−2i2−i21+i−1−i1−i−1+i0000
χ6622-2-2−2i2i−2i2i22-2−2i2i00002-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000−22−i2i2−1−i1+i−1+i1−i0000
χ6722-2-2−2i2i−2i2i22-2−2i2i00002-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000002−2i2−i2−1−i1+i−1+i1−i0000
χ6822-2-2−2i2i−2i2i22-2−2i2i00002-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000−22−i2i21+i−1−i1−i−1+i0000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.