Finite Group Databasebeta

← Group #11778261

Character table — Group #11778261

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444448888888888888888888888888121224242424242424242424242424242424242424484872727272
order1222223366666666663446666666661212441212121212121212121212121212121212121212121212224444466881212121212122424242412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-111-111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-11-1-11-1-111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-111-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-111-1-1
χ92222222222222222222-2-2222222222-2-2000000-2-2-2-2-2-2-200000000000022-200002200-2-200000000000000
χ102222222222222222222-2-2222222222-2-2000000-2-2-2-2-2-2-2000000000000-2-220000-2-2002200000000000000
χ112222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-12222-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12220220-1-100-1-1-1-1-1-10000000000
χ122222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-12222-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-20-2-2011001111110000000000
χ132222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-122-2-211112-1-1-1-1-1-1-2-2-2-2111111112220-2-20-1-100-1-111110000000000
χ142222222-12-1-1-1-1-12-12-1-1222-1-1-1-12-1-1-122-2-211112-1-1-1-1-1-1-2-2-2-211111111-2-2-20220110011-1-1-1-10000000000
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−i3i3i3i3i322-20000-1-10011−i3−i3i3i30000000000
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−i3i3i3i3i3-2-2200001100-1-1i3i3−i3−i30000000000
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−i322-20000-1-10011i3i3−i3−i30000000000
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−i3-2-2200001100-1-1−i3−i3i3i30000000000
χ19222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100020020022000000-1-1-1-1-1-10000
χ20222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-200-200-2-20000001111110000
χ21222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-122-1-1-1-1111111111111000200200-2-20000001111-1-10000
χ22222222-12-122222-12-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-122-1-1-1-1111111111111000-200-20022000000-1-1-1-1110000
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
χ252222-2-22222-2-2-2-222222-22-222-2-2-22-2-2-2-20000002-22-2-222000000000000000200-2000000000000002-20000
χ262222-2-22222-2-2-2-222222-22-222-2-2-22-2-2-2-20000002-22-2-222000000000000000-200200000000000000-220000
χ272222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-133−3−333−3−333−3−3000200-2000000000033−3−3-110000
χ282222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-133−3−333−3−333−3−3000-20020000000000−3−3331-10000
χ292222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-1−3−333−3−333−3−333000200-20000000000−3−333-110000
χ302222-2-2-12-12-2-2-2-2-12-12-1-221-1-1111-11111000000-1-2211-1-1−3−333−3−333−3−333000-2002000000000033−3−31-10000
χ3122-2-22-2222222-2-2-2-2-2-220022-222-2-2-2-20000000000000000000000000002-2000002-22−20000002−22−200002−2
χ3222-2-22-2222222-2-2-2-2-2-220022-222-2-2-2-20000000000000000000000000002-2000002-2−22000000−22−220000−22
χ3322-2-22-2222222-2-2-2-2-2-220022-222-2-2-2-2000000000000000000000000000-2200000-222−20000002−22−20000−22
χ3422-2-22-2222222-2-2-2-2-2-220022-222-2-2-2-2000000000000000000000000000-2200000-22−22000000−22−2200002−2
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
χ4744-4-44-44-24-2-2-222-42-42-2004-22-2-2-42220000000000000000000000000004-400000-22000000000000000000
χ4844-4-44-44-24-2-2-222-42-42-2004-22-2-2-4222000000000000000000000000000-44000002-2000000000000000000
χ4944-4-44-4-24-2444-4-42-42-4-200-2-22-2-2222200000000000000000000000000000000000022−22000000−22−22000000
χ5044-4-44-4-24-2444-4-42-42-4-200-2-22-2-22222000000000000000000000000000000000000−22220000002−22−2000000
χ5144-4-4-444444-4-444-4-4-4-4400-44-4-4-44-444000000000000000000000000000000000000000000000000000000
χ5244-4-4-444-24-222-2-2-42-42-200-4-222242-2-20000000000000000000000000000000000000023−2300000000000000
χ5344-4-4-444-24-222-2-2-42-42-200-4-222242-2-200000000000000000000000000000000000000−232300000000000000
χ5444-4-4-44-24-24-4-4442-42-4-2002-2222-22-2-2000000000000000000000000000000000000000000006−6−66000000
χ5544-4-4-44-24-24-4-4442-42-4-2002-2222-22-2-200000000000000000000000000000000000000000000−666−6000000
χ564-44-40044-4-4000044-4-44000-44000-400002i−2i2i−2i2i−2i00000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000
χ574-44-40044-4-4000044-4-44000-44000-40000−2i2i−2i2i−2i2i0000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000
χ584-44-4004-2-42−2i32i3−2i32i34-2-42-20002-2−2i32i302−2i32i3002i−2i2ζ14−2ζ142ζ22−2ζ2200000002i−2i2i−2i2ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000000000000000000
χ594-44-4004-2-42−2i32i3−2i32i34-2-42-20002-2−2i32i302−2i32i300−2i2i−2ζ142ζ14−2ζ222ζ220000000−2i2i−2i2i−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000000000000000000
χ604-44-4004-2-422i3−2i32i3−2i34-2-42-20002-22i3−2i3022i3−2i3002i−2i2ζ22−2ζ222ζ14−2ζ1400000002i−2i2i−2i2ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000000000000000000
χ614-44-4004-2-422i3−2i32i3−2i34-2-42-20002-22i3−2i3022i3−2i300−2i2i−2ζ222ζ22−2ζ142ζ140000000−2i2i−2i2i−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000000000000000000
χ624-44-400-242-40000-242-4-20002-200020023−232i−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
χ634-44-400-242-40000-242-4-20002-200020023−23−2i2i−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
χ644-44-400-242-40000-242-4-20002-2000200−23232i−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
χ654-44-400-242-40000-242-4-20002-2000200−2323−2i2i−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
χ664-44-400-2-222−2i32i3−2i32i3-2-2221000-11i3−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
χ674-44-400-2-222−2i32i3−2i32i3-2-2221000-11i3−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
χ684-44-400-2-222−2i32i3−2i32i3-2-2221000-11i3−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
χ694-44-400-2-222−2i32i3−2i32i3-2-2221000-11i3−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
χ704-44-400-2-2222i3−2i32i3−2i3-2-2221000-11−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
χ714-44-400-2-2222i3−2i32i3−2i3-2-2221000-11−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
χ724-44-400-2-2222i3−2i32i3−2i3-2-2221000-11−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
χ734-44-400-2-2222i3−2i32i3−2i3-2-2221000-11−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
χ744-4-440044-4-40000-4-4444000-4-400040000000000000000000000000000000002-200000002-22-20000000000
χ754-4-440044-4-40000-4-4444000-4-40004000000000000000000000000000000000-220000000-22-220000000000
χ764-4-44004-2-42−2i32i32i3−2i3-424-2-200022−2i32i30-22i3−2i300000000000000000000000000000002-20000000−1+i31−i3−1−i31+i30000000000
χ774-4-44004-2-42−2i32i32i3−2i3-424-2-200022−2i32i30-22i3−2i30000000000000000000000000000000-2200000001−i3−1+i31+i3−1−i30000000000
χ784-4-44004-2-422i3−2i3−2i32i3-424-2-2000222i3−2i30-2−2i32i300000000000000000000000000000002-20000000−1−i31+i3−1+i31−i30000000000
χ794-4-44004-2-422i3−2i3−2i32i3-424-2-2000222i3−2i30-2−2i32i30000000000000000000000000000000-2200000001+i3−1−i31−i3−1+i30000000000
χ8088-8-88-8-4-4-4-4-4-4444444200-42-2224-2-2-2000000000000000000000000000000000000000000000000000000
χ8188-8-8-88-4-4-4-444-4-4444420042-2-2-2-4-222000000000000000000000000000000000000000000000000000000
χ828-8-8800-484-800004-8-48-400044000-400000000000000000000000000000000000000000000000000000000
χ838-8-8800-4-444−4i34i34i3−4i344-4-42000-2-22i3−2i302−2i32i3000000000000000000000000000000000000000000000000000000
χ848-8-8800-4-4444i3−4i3−4i34i344-4-42000-2-2−2i32i3022i3−2i3000000000000000000000000000000000000000000000000000000

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