Finite Group Databasebeta

← Group #10705335

Character table — Group #10705335

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order124422234446661212121222446666668888121212121212444444448812121212121212121212121212121212242424242424242416161616161616162444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11iiii−i−i−i−i11iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1
χ6111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11iiii−i−i−i−i11iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111
χ7111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11−i−i−i−iiiii11−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1iiii−i−i−i−i-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11−i−i−i−iiiii11−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii11-1-1
χ911-1-1-1-1111-11-1-1111-1-11-11-11-111-1-111-1-1-111-1-11ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-11-1
χ1011-1-1-1-1111-11-1-1111-1-11-11-11-111-1-111-1-1-111-1-11ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1−i−iii−i−iii-11-11
χ1111-1-1-1-1111-11-1-1111-1-11-11-11-111-1-111-1-1-111-1-11−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1ii−i−iii−i−i-11-11
χ1211-1-1-1-1111-11-1-1111-1-11-11-11-111-1-111-1-1-111-1-11−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-11-1
χ1311-1-1-1-1111-11-1-1111-1-1-11-111-1-1-111-1-111-1-1-111111-1-1-1-1111-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111-1-11
χ1411-1-1-1-1111-11-1-1111-1-1-11-111-1-1-111-1-111-1-1-111111-1-1-1-1111-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-111-1
χ1511-1-1-1-1111-11-1-1111-1-1-11-111-1-1-111-1-111-1-1-1111-1-11111-1-11-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111-111-1
χ1611-1-1-1-1111-11-1-1111-1-1-11-111-1-1-111-1-111-1-1-1111-1-11111-1-11-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-11-1-11
χ172222222222222222222222222222-2-2-2-222222200000000-2-20000000000000000-2-2-2-2-2-2-2-2000000000000
χ18222222222222222222-2-2-2-222-2-2-2-222222-2-2-2-2200000000-2-20000000000000000-2-2-2-22222000000000000
χ192222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ202222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-2221111111111111111-1-1-1-1-1-1-1-1000000000000
χ212222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-100000000-2-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311111111000000000000
χ222222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-100000000-2-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311111111000000000000
χ232222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-111112222-11111-100000000-2-233−3−333−3−3−3−333−3−3331111-1-1-1-1000000000000
χ242222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-111112222-11111-100000000-2-2−3−333−3−33333−3−333−3−31111-1-1-1-1000000000000
χ252222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111-2-2-2-2-11111-12i2i2i2i−2i−2i−2i−2i22−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111000000000000
χ262222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-11111-2-2-2-2-11111-1−2i−2i−2i−2i2i2i2i2i22iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111000000000000
χ2722222-2-222-2-222222220000-2-200002i−2i2i−2i-20000-21+i−1−i1+i−1−i1−i−1+i1−i−1+i001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00002i−2i2i−2i000000000000
χ2822222-2-222-2-222222220000-2-200002i−2i2i−2i-20000-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00002i−2i2i−2i000000000000
χ2922222-2-222-2-222222220000-2-20000−2i2i−2i2i-20000-21−i−1+i1−i−1+i1+i−1−i1+i−1−i001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i0000−2i2i−2i2i000000000000
χ3022222-2-222-2-222222220000-2-20000−2i2i−2i2i-20000-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i0000−2i2i−2i2i000000000000
χ3122222-2-2-12-2-2-1-1-1-1-1-1-1000011−i3i3−i3i32i−2i2i−2i1−i3i3−i3i311+i−1−i1+i−1−i1−i−1+i1−i−1+i00−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ223−33−3−ii−ii000000000000
χ3222222-2-2-12-2-2-1-1-1-1-1-1-1000011−i3i3−i3i32i−2i2i−2i1−i3i3−i3i31−1−i1+i−1−i1+i−1+i1−i−1+i1−i00ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ223−33−3−ii−ii000000000000
χ3322222-2-2-12-2-2-1-1-1-1-1-1-1000011−i3i3−i3i3−2i2i−2i2i1−i3i3−i3i311−i−1+i1−i−1+i1+i−1−i1+i−1−i00−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−33−33i−ii−i000000000000
χ3422222-2-2-12-2-2-1-1-1-1-1-1-1000011−i3i3−i3i3−2i2i−2i2i1−i3i3−i3i31−1+i1−i−1+i1−i−1−i1+i−1−i1+i00ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−33−33i−ii−i000000000000
χ3522222-2-2-12-2-2-1-1-1-1-1-1-1000011i3−i3i3−i32i−2i2i−2i1i3−i3i3−i311+i−1−i1+i−1−i1−i−1+i1−i−1+i00−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−33−33−ii−ii000000000000
χ3622222-2-2-12-2-2-1-1-1-1-1-1-1000011i3−i3i3−i32i−2i2i−2i1i3−i3i3−i31−1−i1+i−1−i1+i−1+i1−i−1+i1−i00ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−33−33−ii−ii000000000000
χ3722222-2-2-12-2-2-1-1-1-1-1-1-1000011i3−i3i3−i3−2i2i−2i2i1i3−i3i3−i311−i−1+i1−i−1+i1+i−1−i1+i−1−i00−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ143−33−3i−ii−i000000000000
χ3822222-2-2-12-2-2-1-1-1-1-1-1-1000011i3−i3i3−i3−2i2i−2i2i1i3−i3i3−i31−1+i1−i−1+i1−i−1−i1+i−1−i1+i00ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ143−33−3i−ii−i000000000000
χ392222-2-222-22-2-2-22-2-2222-2-222-222-2-200002-2-222-20000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ402222-2-222-22-2-2-22-2-2222-2-222-222-2-200002-2-222-20000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ412222-2-222-22-2-2-22-2-222-222-22-2-2-2220000222-2-2-200000000000000000000000000000000002−22−2−22−220000
χ422222-2-222-22-2-2-22-2-222-222-22-2-2-2220000222-2-2-20000000000000000000000000000000000−22−222−22−20000
χ4322-2-22222-2-2-2222-2-2-2-222-2-22222220000-2-2-2-2-2-200000000000000000000000000000000002−2−222−2−220000
χ4422-2-22222-2-2-2222-2-2-2-222-2-22222220000-2-2-2-2-2-20000000000000000000000000000000000−222−2−222−20000
χ4522-2-22222-2-2-2222-2-2-2-2-2-22222-2-2-2-20000-22222-20000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ4622-2-22222-2-2-2222-2-2-2-2-2-22222-2-2-2-20000-22222-20000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ4722-2-2-22-2222-2-2-2222-2-20000-2200002i−2i−2i2i20000-21−i−1+i−1+i1−i−1−i1+i1+i−1−i001−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i00002i−2i−2i2i000000000000
χ4822-2-2-22-2222-2-2-2222-2-20000-2200002i−2i−2i2i20000-2−1+i1−i1−i−1+i1+i−1−i−1−i1+i00−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00002i−2i−2i2i000000000000
χ4922-2-2-22-2222-2-2-2222-2-20000-220000−2i2i2i−2i20000-21+i−1−i−1−i1+i−1+i1−i1−i−1+i001+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i0000−2i2i2i−2i000000000000
χ5022-2-2-22-2222-2-2-2222-2-20000-220000−2i2i2i−2i20000-2−1−i1+i1+i−1−i1−i−1+i−1+i1−i00−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i0000−2i2i2i−2i000000000000
χ5122-2-2-22-2-122-211-1-1-11100001-1−i3i3i3−i32i−2i−2i2i-1−i3i3i3−i311−i−1+i−1+i1−i−1−i1+i1+i−1−i00−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ143−3−33−iii−i000000000000
χ5222-2-2-22-2-122-211-1-1-11100001-1−i3i3i3−i32i−2i−2i2i-1−i3i3i3−i31−1+i1−i1−i−1+i1+i−1−i−1−i1+i00ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ143−3−33−iii−i000000000000
χ5322-2-2-22-2-122-211-1-1-11100001-1−i3i3i3−i3−2i2i2i−2i-1−i3i3i3−i311+i−1−i−1−i1+i−1+i1−i1−i−1+i00−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−333−3i−i−ii000000000000
χ5422-2-2-22-2-122-211-1-1-11100001-1−i3i3i3−i3−2i2i2i−2i-1−i3i3i3−i31−1−i1+i1+i−1−i1−i−1+i−1+i1−i00ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14−333−3i−i−ii000000000000
χ5522-2-2-22-2-122-211-1-1-11100001-1i3−i3−i3i32i−2i−2i2i-1i3−i3−i3i311−i−1+i−1+i1−i−1−i1+i1+i−1−i00−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−333−3−iii−i000000000000
χ5622-2-2-22-2-122-211-1-1-11100001-1i3−i3−i3i32i−2i−2i2i-1i3−i3−i3i31−1+i1−i1−i−1+i1+i−1−i−1−i1+i00ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−333−3−iii−i000000000000
χ5722-2-2-22-2-122-211-1-1-11100001-1i3−i3−i3i3−2i2i2i−2i-1i3−i3−i3i311+i−1−i−1−i1+i−1+i1−i1−i−1+i00−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ223−3−33i−i−ii000000000000
χ5822-2-2-22-2-122-211-1-1-11100001-1i3−i3−i3i3−2i2i2i−2i-1i3−i3−i3i31−1−i1+i1+i−1−i1−i−1+i−1+i1−i00ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ223−3−33i−i−ii000000000000
χ5922-2-2-2-2222-22-2-2222-2-22-22-22-222-2-2-2-222-222-2-2200000000-220000000000000000-2-222-2-222000000000000
χ6022-2-2-2-2222-22-2-2222-2-2-22-222-2-2-22222-2-2-2-2-222200000000-220000000000000000-2-22222-2-2000000000000
χ6122-2-2-2-22-12-2211-1-1-1112-22-2-11-1-11122-2-21-1-111-12i2i−2i−2i2i2i−2i−2i2-2−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111000000000000
χ6222-2-2-2-22-12-2211-1-1-1112-22-2-11-1-11122-2-21-1-111-1−2i−2i2i2i−2i−2i2i2i2-2iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111000000000000
χ6322-2-2-2-22-12-2211-1-1-1112-22-2-11-1-111-2-2221-1-111-100000000-2233−3−3−3−33333−3−3−3−33311-1-111-1-1000000000000
χ6422-2-2-2-22-12-2211-1-1-1112-22-2-11-1-111-2-2221-1-111-100000000-22−3−33333−3−3−3−33333−3−311-1-111-1-1000000000000
χ6522-2-2-2-22-12-2211-1-1-111-22-22-1111-1-122-2-2111-1-1-100000000-22−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-111000000000000
χ6622-2-2-2-22-12-2211-1-1-111-22-22-1111-1-122-2-2111-1-1-100000000-22i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-111000000000000
χ6722-2-2-2-22-12-2211-1-1-111-22-22-1111-1-1-2-222111-1-1-122-2-2-2-2222-2-1-1-1-111111111-1-1-1-1-1-11111-1-1000000000000
χ6822-2-2-2-22-12-2211-1-1-111-22-22-1111-1-1-2-222111-1-1-1-2-22222-2-22-21111-1-1-1-1-1-1-1-11111-1-11111-1-1000000000000
χ694444-44-44-4-44-4-44-4-4440000-4400000000-4000040000000000000000000000000000000000000000000000
χ704444-44-4-2-4-4422-222-2-200002-2−2i32i32i3−2i3000022i3−2i3−2i32i3-20000000000000000000000000000000000000000000000
χ714444-44-4-2-4-4422-222-2-200002-22i3−2i3−2i32i300002−2i32i32i3−2i3-20000000000000000000000000000000000000000000000
χ724444-4-44-2-44-422-222-2-24-4-44-22-2-2220000-222-2-220000000000000000000000000000000000000000000000
χ734444-4-44-2-44-422-222-2-2-444-4-2222-2-20000-2-2-22220000000000000000000000000000000000000000000000
χ7444-4-4444-2-4-4-4-2-2-2222244-4-4-2-2-2-2-2-200002222220000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-2-2-22222-4-444-2-2222200002-2-2-2-220000000000000000000000000000000000000000000000
χ7644-4-44-4-44-444444-4-4-4-40000-4-4000000004000040000000000000000000000000000000000000000000000
χ7744-4-44-4-4-2-444-2-2-22222000022−2i32i3−2i32i30000-22i3−2i32i3−2i3-20000000000000000000000000000000000000000000000
χ7844-4-44-4-4-2-444-2-2-222220000222i3−2i32i3−2i30000-2−2i32i3−2i32i3-20000000000000000000000000000000000000000000000
χ798-88i−8i000800000-8008i−8i000000000000000000000000000000000000000000000000000000000000000000
χ808-88i−8i000-4000−4i34i3443−43−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ818-88i−8i000-40004i3−4i34−4343−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ828-8−8i8i000800000-800−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000-4000−4i34i34−43434i−4i000000000000000000000000000000000000000000000000000000000000000000
χ848-8−8i8i000-40004i3−4i3443−434i−4i000000000000000000000000000000000000000000000000000000000000000000

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