Finite Group Databasebeta

← Group #11778074

Character table — Group #11778074

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order12222233666666666634466666666612124412121212121212121212121212121212121212121212124422444666688121212122424242412122488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11111111111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1-1-11111-1-111-1-1
χ92222222222222222222-2-2222222222-2-2000000-2-2-2-2-2-2-2000000000000220000-2000000-2-2220000000000
χ102222222222222222222-2-2222222222-2-2000000-2-2-2-2-2-2-2000000000000-2-20000200000022-2-20000000000
χ112222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-12222-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222002-1-1-1-100-1-1-1-10000000000
χ122222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-12222-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200-211110011110000000000
χ132222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-122-2-211112-1-1-1-1-1-1-2-2-2-21111111122-2-2002111100-1-1-1-10000000000
χ142222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-122-2-211112-1-1-1-1-1-1-2-2-2-211111111-2-22200-2-1-1-1-10011110000000000
χ152222222-12-1-1-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200−i3−i3i3i3-21111110000−i3−i3−i3−i3i3i3i3i3220000-2−i3−i3i3i30011-1-10000000000
χ162222222-12-1-1-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200−i3−i3i3i3-21111110000−i3−i3−i3−i3i3i3i3i3-2-200002i3i3−i3−i300-1-1110000000000
χ172222222-12-1-1-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200i3i3−i3−i3-21111110000i3i3i3i3−i3−i3−i3−i3220000-2i3i3−i3−i30011-1-10000000000
χ182222222-12-1-1-1-1-12-12-1-1-2-22-1-1-1-12-1-1-1-2-200i3i3−i3−i3-21111110000i3i3i3i3−i3−i3−i3−i3-2-200002−i3−i3i3i300-1-1110000000000
χ19222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100002200000220000-1-1-1-1-1-10000
χ20222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-200000-2-200001111110000
χ21222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-122-1-1-1-111111111111100002200000-2-200001111-1-10000
χ22222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-122-1-1-1-11111111111110000-2-200000220000-1-1-1-1110000
χ232222-2-22222-2-2-2-2222222-2-222-2-2-22-2-222000000-22-222-2-2000000000000000000000000000000000002-200
χ242222-2-22222-2-2-2-2222222-2-222-2-2-22-2-222000000-22-222-2-200000000000000000000000000000000000-2200
χ252222-2-22222-2-2-2-222222-22-222-2-2-22-2-2-2-20000002-22-2-22200000000000000002-20000000000000002-20000
χ262222-2-22222-2-2-2-222222-22-222-2-2-22-2-2-2-20000002-22-2-2220000000000000000-22000000000000000-220000
χ272222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-133−3−333−3−333−3−300002-20000000000033−3−3-110000
χ282222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-133−3−333−3−333−3−30000-2200000000000−3−3331-10000
χ292222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-1−3−333−3−333−3−33300002-200000000000−3−333-110000
χ302222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-1−3−333−3−333−3−3330000-220000000000033−3−31-10000
χ312-2-222-2222-222-2-2-22-2-220022-222-2-2-2-20000000000000000000000000002i−2i0000000002−2002i−2i2−22−20000−i2i2
χ322-2-222-2222-222-2-2-22-2-220022-222-2-2-2-20000000000000000000000000002i−2i000000000−22002i−2i−22−220000i2−i2
χ332-2-222-2222-222-2-2-22-2-220022-222-2-2-2-2000000000000000000000000000−2i2i0000000002−200−2i2i2−22−20000i2−i2
χ342-2-222-2222-222-2-2-22-2-220022-222-2-2-2-2000000000000000000000000000−2i2i000000000−2200−2i2i−22−220000−i2i2
χ35444444-24-244444-24-24-2-4-4-2-2-2-2-2-2-2-2-2220000002-4-42222000000000000000000000000000000000000000
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
χ37444444-2-2-2-2-2-2-2-2-2-2-2-2144-21111-2111-2-2-4-42222-2-2-211112222-1-1-1-1-1-1-1-1000000000000000000000000000
χ38444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-21112200−2i3−2i32i32i3222-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000000000000000000000000000
χ39444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-21111-211122002i32i3−2i3−2i3222-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000000000000000000000000000
χ404444-4-44-24-222224-24-2-24-4-4-2-222-4-22244000000-4-22-2-222000000000000000000000000000000000000000
χ414444-4-44-24-222224-24-2-2-44-4-2-222-4-222-4-400000042-222-2-2000000000000000000000000000000000000000
χ424444-4-4-24-24-4-4-4-4-24-24-24-42-2-2222-222-2-200000024-4-2-222000000000000000000000000000000000000000
χ434444-4-4-2-2-2-22222-2-2-2-214-4211-1-121-1-1-2-20000002-2211-1-100003i3i−3i−3i−3i−3i3i3i000000000000000000000000000
χ444444-4-4-2-2-2-22222-2-2-2-214-4211-1-121-1-1-2-20000002-2211-1-10000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000
χ454444-4-4-2-2-2-22222-2-2-2-21-44211-1-121-1-122000000-22-2-1-1112323−23−23−3−333−3−333000000000000000000000000000
χ464444-4-4-2-2-2-22222-2-2-2-21-44211-1-121-1-122000000-22-2-1-111−23−23232333−3−333−3−3000000000000000000000000000
χ4744-4-40044-4400004-4-4-44000-44000-400002i−2i2i−2i2i−2i00000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000
χ4844-4-40044-4400004-4-4-44000-44000-40000−2i2i−2i2i−2i2i0000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000
χ4944-4-4004-2-4-2−2i32i3−2i32i342-42-20002-2−2i32i302−2i32i3002i−2i2ζ14−2ζ142ζ22−2ζ2200000002i−2i2i−2i2ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000000
χ5044-4-4004-2-4-2−2i32i3−2i32i342-42-20002-2−2i32i302−2i32i300−2i2i−2ζ142ζ14−2ζ222ζ220000000−2i2i−2i2i−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000000
χ5144-4-4004-2-4-22i3−2i32i3−2i342-42-20002-22i3−2i3022i3−2i3002i−2i2ζ22−2ζ222ζ14−2ζ1400000002i−2i2i−2i2ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000000
χ5244-4-4004-2-4-22i3−2i32i3−2i342-42-20002-22i3−2i3022i3−2i300−2i2i−2ζ222ζ22−2ζ142ζ140000000−2i2i−2i2i−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000000
χ5344-4-400-24240000-2-42-4-20002-200020023−232i−2i2i−2i2i−2i00023−2300−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000000
χ5444-4-400-24240000-2-42-4-20002-200020023−23−2i2i−2i2i−2i2i00023−2300ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000000
χ5544-4-400-24240000-2-42-4-20002-2000200−23232i−2i2i−2i2i−2i000−232300ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000000
χ5644-4-400-24240000-2-42-4-20002-2000200−2323−2i2i−2i2i−2i2i000−232300−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000000
χ5744-4-400-2-22-2−2i32i3−2i32i3-22221000-11i3−i30-1i3−i323−232i−2i2ζ14−2ζ142ζ22−2ζ22000−333i−3i−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ202ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22−2ζ4−ζ20−ζ222ζ4+ζ20+ζ22000000000000000000000000000
χ5844-4-400-2-22-2−2i32i3−2i32i3-22221000-11i3−i30-1i3−i323−23−2i2i−2ζ142ζ14−2ζ222ζ22000−333i−3iζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ20−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20−2ζ4−ζ20+ζ222ζ4+ζ20−ζ222ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22000000000000000000000000000
χ5944-4-400-2-22-2−2i32i3−2i32i3-22221000-11i3−i30-1i3−i3−23232i−2i2ζ14−2ζ142ζ22−2ζ220003−3−3i3iζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ20−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20−2ζ4−ζ20−ζ222ζ4+ζ20+ζ222ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22000000000000000000000000000
χ6044-4-400-2-22-2−2i32i3−2i32i3-22221000-11i3−i30-1i3−i3−2323−2i2i−2ζ142ζ14−2ζ222ζ220003−3−3i3i−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ202ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22−2ζ4−ζ20+ζ222ζ4+ζ20−ζ22000000000000000000000000000
χ6144-4-400-2-22-22i3−2i32i3−2i3-22221000-11−i3i30-1−i3i323−232i−2i2ζ22−2ζ222ζ14−2ζ14000−33−3i3i−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ222ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22−2ζ4−ζ20−ζ222ζ4+ζ20+ζ22−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ20000000000000000000000000000
χ6244-4-400-2-22-22i3−2i32i3−2i3-22221000-11−i3i30-1−i3i323−23−2i2i−2ζ222ζ22−2ζ142ζ14000−33−3i3iζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−2ζ4−ζ20+ζ222ζ4+ζ20−ζ222ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ20−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20000000000000000000000000000
χ6344-4-400-2-22-22i3−2i32i3−2i3-22221000-11−i3i30-1−i3i3−23232i−2i2ζ22−2ζ222ζ14−2ζ140003−33i−3iζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−2ζ4−ζ20−ζ222ζ4+ζ20+ζ222ζ4+ζ20−ζ22−2ζ4−ζ20+ζ22ζ4−ζ14+2ζ20−ζ4+ζ14−2ζ20−ζ4−ζ14−2ζ20ζ4+ζ14+2ζ20000000000000000000000000000
χ6444-4-400-2-22-22i3−2i32i3−2i3-22221000-11−i3i30-1−i3i3−2323−2i2i−2ζ222ζ22−2ζ142ζ140003−33i−3i−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ222ζ4+ζ20+ζ22−2ζ4−ζ20−ζ22−2ζ4−ζ20+ζ222ζ4+ζ20−ζ22−ζ4+ζ14−2ζ20ζ4−ζ14+2ζ20ζ4+ζ14+2ζ20−ζ4−ζ14−2ζ20000000000000000000000000000
χ654-44-40044-4-40000-4-4444000-4-4000400000000000000000000000000000002-20002-22-20000000000000000
χ664-44-40044-4-40000-4-4444000-4-400040000000000000000000000000000000-22000-22-220000000000000000
χ674-44-4004-2-42−2i32i32i3−2i3-424-2-200022−2i32i30-22i3−2i3000000000000000000000000000002-2000−1+i31−i3−1−i31+i30000000000000000
χ684-44-4004-2-42−2i32i32i3−2i3-424-2-200022−2i32i30-22i3−2i300000000000000000000000000000-220001−i3−1+i31+i3−1−i30000000000000000
χ694-44-4004-2-422i3−2i3−2i32i3-424-2-2000222i3−2i30-2−2i32i3000000000000000000000000000002-2000−1−i31+i3−1+i31−i30000000000000000
χ704-44-4004-2-422i3−2i3−2i32i3-424-2-2000222i3−2i30-2−2i32i300000000000000000000000000000-220001+i3−1−i31−i3−1+i30000000000000000
χ714-4-444-44-242-2-222-4-2-42-2004-22-2-2-42220000000000000000000000000004i−4i0000000000000−2i2i0000000000
χ724-4-444-44-242-2-222-4-2-42-2004-22-2-2-4222000000000000000000000000000−4i4i00000000000002i−2i0000000000
χ734-4-444-4-24-2-444-4-4242-4-200-2-22-2-222220000000000000000000000000000000000000022−220000−22−22000000
χ744-4-444-4-24-2-444-4-4242-4-200-2-22-2-2222200000000000000000000000000000000000000−222200002−22−2000000
χ754-4-44-44444-4-4-444-44-4-4400-44-4-4-44-444000000000000000000000000000000000000000000000000000000
χ764-4-44-444-24222-2-2-4-2-42-200-4-222242-2-20000000000000000000000000000000000000000−2i32i3000000000000
χ774-4-44-444-24222-2-2-4-2-42-200-4-222242-2-200000000000000000000000000000000000000002i3−2i3000000000000
χ784-4-44-44-24-2-4-4-444242-4-2002-2222-22-2-2000000000000000000000000000000000000000000006−6−66000000
χ794-4-44-44-24-2-4-4-444242-4-2002-2222-22-2-200000000000000000000000000000000000000000000−666−6000000
χ808-88-800-484-800004-8-48-400044000-400000000000000000000000000000000000000000000000000000000
χ818-88-800-4-444−4i34i34i3−4i344-4-42000-2-22i3−2i302−2i32i3000000000000000000000000000000000000000000000000000000
χ828-88-800-4-4444i3−4i3−4i34i344-4-42000-2-2−2i32i3022i3−2i3000000000000000000000000000000000000000000000000000000
χ838-8-888-8-4-4-44-4-4444-444200-42-2224-2-2-2000000000000000000000000000000000000000000000000000000
χ848-8-88-88-4-4-4444-4-44-44420042-2-2-2-4-222000000000000000000000000000000000000000000000000000000

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