Finite Group Databasebeta

← Group #11778528

Character table — Group #11778528

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order12222233666666666634466666666612124412121212121212121212121212121212121212121212124424444881212121212121212242424246124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1111-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-11-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1111111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111-1-111-1-1
χ92222222222222222222-2-2222222222-2-200-20000-2-2-2-2-2-2000000000000220-20000022-2-200000000000000
χ102222222222222222222-2-2222222222-2-200-20000-2-2-2-2-2-2000000000000-2-20200000-2-22200000000000000
χ112222222-1222-122-1-122-122-1-1-1-1-1-1-1-1-1-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100200022200000000-1-1-1-1-1-10000
χ122222222-1222-122-1-122-122-1-1-1-1-1-1-1-1-1-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2000-2-2-2000000001111110000
χ132222222-1222-122-1-122-122-1-1-1-1-1-1-1-1-1-1-1-2-2-1-2-2-2-222-1-1-1-11111111111110020002-2-2000000001111-1-10000
χ142222222-1222-122-1-122-122-1-1-1-1-1-1-1-1-1-1-1-2-2-1-2-2-2-222-1-1-1-111111111111100-2000-22200000000-1-1-1-1110000
χ15222222-12-1-1-12-1-122-1-1-1222-1-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1220222000-1-1-1-1-1-1-1-10000000000
χ16222222-12-1-1-12-1-122-1-1-1222-1-1-1-12-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-20-2-2-2000111111110000000000
χ17222222-12-1-1-12-1-122-1-1-1222-1-1-1-12-1-1-122-2-221111-1-1-1-1-1-1-2-2-2-2111111112202-2-2000-1-1-1-111110000000000
χ18222222-12-1-1-12-1-122-1-1-1222-1-1-1-12-1-1-122-2-221111-1-1-1-1-1-1-2-2-2-211111111-2-20-2220001111-1-1-1-10000000000
χ19222222-12-1-1-12-1-122-1-1-1-2-22-1-1-1-12-1-1-1-2-200-2−i3−i3i3i31111110000−i3−i3−i3−i3i3i3i3i3220-200000-1-111−i3−i3i3i30000000000
χ20222222-12-1-1-12-1-122-1-1-1-2-22-1-1-1-12-1-1-1-2-200-2−i3−i3i3i31111110000−i3−i3−i3−i3i3i3i3i3-2-2020000011-1-1i3i3−i3−i30000000000
χ21222222-12-1-1-12-1-122-1-1-1-2-22-1-1-1-12-1-1-1-2-200-2i3i3−i3−i31111110000i3i3i3i3−i3−i3−i3−i3220-200000-1-111i3i3−i3−i30000000000
χ22222222-12-1-1-12-1-122-1-1-1-2-22-1-1-1-12-1-1-1-2-200-2i3i3−i3−i31111110000i3i3i3i3−i3−i3−i3−i3-2-2020000011-1-1−i3−i3i3i30000000000
χ232222-2-2222-2-22-2-2222222-2-222-2-2-22-2-22200-200002-222-2-2000000000000000000000000000000000002-200
χ242222-2-2222-2-22-2-2222222-2-222-2-2-22-2-22200-200002-222-2-200000000000000000000000000000000000-2200
χ252222-2-2222-2-22-2-222222-22-222-2-2-22-2-2-2-20020000-22-2-222000000000000002000-2000000000000002-20000
χ262222-2-2222-2-22-2-222222-22-222-2-2-22-2-2-2-20020000-22-2-22200000000000000-2000200000000000000-220000
χ272222-2-22-12-2-2-1-2-2-1-122-1-221-1-1111-1111100-10000-2211-1-133−3−333−3−333−3−3002000-2000000000033−3−3-110000
χ282222-2-22-12-2-2-1-2-2-1-122-1-221-1-1111-1111100-10000-2211-1-133−3−333−3−333−3−300-200020000000000−3−3331-10000
χ292222-2-22-12-2-2-1-2-2-1-122-1-221-1-1111-1111100-10000-2211-1-1−3−333−3−333−3−333002000-20000000000−3−333-110000
χ302222-2-22-12-2-2-1-2-2-1-122-1-221-1-1111-1111100-10000-2211-1-1−3−333−3−333−3−33300-20002000000000033−3−31-10000
χ312-22-22-222-222-2-2-2-22-2220022-222-2-2-2-20000000000000000000000000002i−2i00000−i2i22i−2i000000−i2i2−i2i200002−2
χ322-22-22-222-222-2-2-2-22-2220022-222-2-2-2-20000000000000000000000000002i−2i00000i2−i22i−2i000000i2−i2i2−i20000−22
χ332-22-22-222-222-2-2-2-22-2220022-222-2-2-2-2000000000000000000000000000−2i2i00000−i2i2−2i2i000000−i2i2−i2i20000−22
χ342-22-22-222-222-2-2-2-22-2220022-222-2-2-2-2000000000000000000000000000−2i2i00000i2−i2−2i2i000000i2−i2i2−i200002−2
χ354444444-2444-244-2-244-2-4-4-2-2-2-2-2-2-2-2-2220020000-4-42222000000000000000000000000000000000000000
χ36444444-2-2-2-2-2-2-2-2-2-2-2-2144-21111-2111-2-244-2-2-2-2-2-2-21111-2-2-2-211111111000000000000000000000000000
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-21111-2111-2-2-4-4-22222-2-211112222-1-1-1-1-1-1-1-1000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-211122002−2i3−2i32i32i322-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-2111220022i32i3−2i3−2i322-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-24-4-4-2-4-4-2-244-24-42-2-2222-222-2-200200004-4-2-222000000000000000000000000000000000000000
χ414444-4-4-24-22242244-2-2-24-4-4-2-222-4-2224400-40000-22-2-222000000000000000000000000000000000000000
χ424444-4-4-24-22242244-2-2-2-44-4-2-222-4-222-4-400400002-222-2-2000000000000000000000000000000000000000
χ434444-4-4-2-2-222-222-2-2-2-214-4211-1-121-1-1-2-20020000-2211-1-100003i3i−3i−3i−3i−3i3i3i000000000000000000000000000
χ444444-4-4-2-2-222-222-2-2-2-214-4211-1-121-1-1-2-20020000-2211-1-10000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000
χ454444-4-4-2-2-222-222-2-2-2-21-44211-1-121-1-12200-200002-2-1-1112323−23−23−3−333−3−333000000000000000000000000000
χ464444-4-4-2-2-222-222-2-2-2-21-44211-1-121-1-12200-200002-2-1-111−23−23232333−3−333−3−3000000000000000000000000000
χ4744-4-40044400400-4-4-4-44000-44000-400002-202-22-20000002-22-22-22-22-22-2000000000000000000000000000
χ4844-4-40044400400-4-4-4-44000-44000-40000-220-22-22000000-22-22-22-22-22-22000000000000000000000000000
χ4944-4-4004-2400-20022-4-4-20002-200020023−232-202-22-20023−2300−1+31−3−1−31+3−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000000
χ5044-4-4004-2400-20022-4-4-20002-200020023−23-220-22-220023−23001−3−1+31+3−1−31−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000000
χ5144-4-4004-2400-20022-4-4-20002-2000200−23232-202-22-200−232300−1−31+3−1+31−3−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000000
χ5244-4-4004-2400-20022-4-4-20002-2000200−2323-220-22-2200−2323001+3−1−31−3−1+31+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000000
χ5344-4-400-24-2−2i32i34−2i32i3-4-422-20002-2−2i32i302−2i32i3002-20−1−i31+i3−1+i31−i30000002-22-2−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000000000000000000000000000
χ5444-4-400-24-2−2i32i34−2i32i3-4-422-20002-2−2i32i302−2i32i300-2201+i3−1−i31−i3−1+i3000000-22-221+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000000000000000000000000000
χ5544-4-400-24-22i3−2i342i3−2i3-4-422-20002-22i3−2i3022i3−2i3002-20−1+i31−i3−1−i31+i30000002-22-2−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000000000000000000000000000
χ5644-4-400-24-22i3−2i342i3−2i3-4-422-20002-22i3−2i3022i3−2i300-2201−i3−1+i31+i3−1−i3000000-22-221−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000000000000000000000000000
χ5744-4-400-2-2-2−2i32i3-2−2i32i322221000-11i3−i30-1i3−i323−232-20−1−i31+i3−1+i31−i300−333i−3i−1+31−3−1−31+3ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ222ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22−2ζ14+ζ20−ζ222ζ14−ζ20+ζ22000000000000000000000000000
χ5844-4-400-2-2-2−2i32i3-2−2i32i322221000-11i3−i30-1i3−i323−23-2201+i3−1−i31−i3−1+i300−333i−3i1−3−1+31+3−1−3−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ22−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22−2ζ14−ζ20−ζ222ζ14+ζ20+ζ222ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22000000000000000000000000000
χ5944-4-400-2-2-2−2i32i3-2−2i32i322221000-11i3−i30-1i3−i3−23232-20−1−i31+i3−1+i31−i3003−3−3i3i−1−31+3−1+31−3ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ22ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22−2ζ14+ζ20−ζ222ζ14−ζ20+ζ222ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22000000000000000000000000000
χ6044-4-400-2-2-2−2i32i3-2−2i32i322221000-11i3−i30-1i3−i3−2323-2201+i3−1−i31−i3−1+i3003−3−3i3i1+3−1−31−3−1+3−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ222ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22−2ζ14−ζ20−ζ222ζ14+ζ20+ζ22000000000000000000000000000
χ6144-4-400-2-2-22i3−2i3-22i3−2i322221000-11−i3i30-1−i3i323−232-20−1+i31−i3−1−i31+i300−33−3i3i−1+31−3−1−31+32ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22−2ζ14+ζ20−ζ222ζ14−ζ20+ζ22ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ22000000000000000000000000000
χ6244-4-400-2-2-22i3−2i3-22i3−2i322221000-11−i3i30-1−i3i323−23-2201−i3−1+i31+i3−1−i300−33−3i3i1−3−1+31+3−1−3−2ζ14−ζ20−ζ222ζ14+ζ20+ζ222ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ22−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22000000000000000000000000000
χ6344-4-400-2-2-22i3−2i3-22i3−2i322221000-11−i3i30-1−i3i3−23232-20−1+i31−i3−1−i31+i3003−33i−3i−1−31+3−1+31−3−2ζ14+ζ20−ζ222ζ14−ζ20+ζ222ζ14+ζ20+ζ22−2ζ14−ζ20−ζ22ζ4+ζ14+2ζ22−ζ4−ζ14−2ζ22ζ4−ζ14−2ζ22−ζ4+ζ14+2ζ22000000000000000000000000000
χ6444-4-400-2-2-22i3−2i3-22i3−2i322221000-11−i3i30-1−i3i3−2323-2201−i3−1+i31+i3−1−i3003−33i−3i1+3−1−31−3−1+32ζ14−ζ20+ζ22−2ζ14+ζ20−ζ22−2ζ14−ζ20−ζ222ζ14+ζ20+ζ22−ζ4−ζ14−2ζ22ζ4+ζ14+2ζ22−ζ4+ζ14+2ζ22ζ4−ζ14−2ζ22000000000000000000000000000
χ654-44-44-44-2-4442-4-42-2-44-200-2-22-2-222220000000000000000000000000000000000−2i22i200000000i2−i2i2−i2000000
χ664-44-44-44-2-4442-4-42-2-44-200-2-22-2-2222200000000000000000000000000000000002i2−2i200000000−i2i2−i2i2000000
χ674-44-44-4-242-2-2-422-442-2-2004-22-2-2-42220000000000000000000000000004i−4i0000000−2i2i0000000000000000
χ684-44-44-4-242-2-2-422-442-2-2004-22-2-2-4222000000000000000000000000000−4i4i00000002i−2i0000000000000000
χ694-44-4-4444-4-4-4-444-44-44400-44-4-4-44-444000000000000000000000000000000000000000000000000000000
χ704-44-4-444-2-4-4-42442-2-44-2002-2222-22-2-200000000000000000000000000000000000000000000i6−i6−i6i6000000
χ714-44-4-444-2-4-4-42442-2-44-2002-2222-22-2-200000000000000000000000000000000000000000000−i6i6i6−i6000000
χ724-44-4-44-24222-4-2-2-442-2-200-4-222242-2-200000000000000000000000000000000000000−2i32i300000000000000
χ734-44-4-44-24222-4-2-2-442-2-200-4-222242-2-2000000000000000000000000000000000000002i3−2i300000000000000
χ744-4-440044-400-4004-44-44000-4-400040000000000000000000000000000000002i−2i00000002i−2i2i−2i0000000000
χ754-4-440044-400-4004-44-44000-4-40004000000000000000000000000000000000−2i2i0000000−2i2i−2i2i0000000000
χ764-4-4400-242−2i32i3-42i3−2i34-4-22-200022−2i32i30-22i3−2i300000000000000000000000000000002i−2i00000002ζ22−2ζ222ζ14−2ζ140000000000
χ774-4-4400-242−2i32i3-42i3−2i34-4-22-200022−2i32i30-22i3−2i30000000000000000000000000000000−2i2i0000000−2ζ222ζ22−2ζ142ζ140000000000
χ784-4-4400-2422i3−2i3-4−2i32i34-4-22-2000222i3−2i30-2−2i32i300000000000000000000000000000002i−2i00000002ζ14−2ζ142ζ22−2ζ220000000000
χ794-4-4400-2422i3−2i3-4−2i32i34-4-22-2000222i3−2i30-2−2i32i30000000000000000000000000000000−2i2i0000000−2ζ142ζ14−2ζ222ζ220000000000
χ808-88-88-8-4-44-4-44444-44-4200-42-2224-2-2-2000000000000000000000000000000000000000000000000000000
χ818-88-8-88-4-44444-4-44-44-420042-2-2-2-4-222000000000000000000000000000000000000000000000000000000
χ828-8-88008-4-800400-448-8-400044000-400000000000000000000000000000000000000000000000000000000
χ838-8-8800-4-44−4i34i344i3−4i3-44-442000-2-22i3−2i302−2i32i3000000000000000000000000000000000000000000000000000000
χ848-8-8800-4-444i3−4i34−4i34i3-44-442000-2-2−2i32i3022i3−2i3000000000000000000000000000000000000000000000000000000

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