Finite Group Databasebeta

← Group #10698516

Character table — Group #10698516

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222222244448888888888888888888888888888888888888888242424242424242448484848
order1222222222223666666666666666444444444444444412121212121212121212121212121212121212121212121212121212888888882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-11
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ92222222222222222222222222222-2-2-2-222-2-200000000-2-2-2-22222-2-2-2-20000000000000000000000000000
χ102222222222222222222222222222-2-2-2-2-2-22200000000-2-2-2-2-2-2-2-222220000000000000000000000000000
χ11222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ12222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000
χ13222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-22222-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-1-1-1-1000000000000
χ14222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000
χ15222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2000000001111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ16222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2000000001111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ17222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2220000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3000000000000
χ18222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2220000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3000000000000
χ1922222222-2-2-2-22222-2-2-2-2-2-2222-2-222-22-200000000000022-2-20000000000000000000000000000000020-20
χ2022222222-2-2-2-22222-2-2-2-2-2-2222-2-222-22-200000000000022-2-200000000000000000000000000000000-2020
χ2122222222-2-2-2-22222-2-2-2-2-2-2222-2-22-22-22000000000000-2-22200000000000000000000000000000000020-2
χ2222222222-2-2-2-22222-2-2-2-2-2-2222-2-22-22-22000000000000-2-222000000000000000000000000000000000-202
χ2322-22-2-2-2222-2-2222-22222-2-22-2-2-2-2-20000002-2000000000000000022-2-20000000000000000−i2−i2i2i2−i2−i2i2i20000
χ2422-22-2-2-2222-2-2222-22222-2-22-2-2-2-2-20000002-2000000000000000022-2-20000000000000000i2i2−i2−i2i2i2−i2−i20000
χ2522-22-2-2-2222-2-2222-22222-2-22-2-2-2-2-2000000-220000000000000000-2-2220000000000000000−i2−i2i2i2i2i2−i2−i20000
χ2622-22-2-2-2222-2-2222-22222-2-22-2-2-2-2-2000000-220000000000000000-2-2220000000000000000i2i2−i2−i2−i2−i2i2i20000
χ272-22-22-2-222-22-222-2222-2-222-22-2-2-2-22-2-220000000000002-22-20000000000000000000000002i−2i2i−2i00000000
χ282-22-22-2-222-22-222-2222-2-222-22-2-2-2-22-2-220000000000002-22-2000000000000000000000000−2i2i−2i2i00000000
χ292-22-22-2-222-22-222-2222-2-222-22-2-2-2-2-222-2000000000000-22-2200000000000000000000000000002i−2i2i−2i0000
χ302-22-22-2-222-22-222-2222-2-222-22-2-2-2-2-222-2000000000000-22-220000000000000000000000000000−2i2i−2i2i0000
χ312-22-22-2-22-22-2222-22-2-222-2-2-22-222-222-2-200002i2i−2i−2i00002-2-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ322-22-22-2-22-22-2222-22-2-222-2-2-22-222-222-2-20000−2i−2i2i2i00002-2-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ332-22-22-2-22-22-2222-22-2-222-2-2-22-222-2-2-2220000000022-2-2-222-20000000022-2-222-2-200000000000000000000
χ342-22-22-2-22-22-2222-22-2-222-2-2-22-222-2-2-22200000000-2-222-222-200000000-2-222-2-22200000000000000000000
χ352-22-22-2-22-22-22-1-11-111-1-1111-11-1-1122-2-200002i2i−2i−2i0000-111-133−3−33−33−3−i3−i3i3i3i3i3−i3−i3−i−iii−i−iii000000000000
χ362-22-22-2-22-22-22-1-11-111-1-1111-11-1-1122-2-200002i2i−2i−2i0000-111-1−3−333−33−33i3i3−i3−i3−i3−i3i3i3−i−iii−i−iii000000000000
χ372-22-22-2-22-22-22-1-11-111-1-1111-11-1-1122-2-20000−2i−2i2i2i0000-111-133−3−33−33−3i3i3−i3−i3−i3−i3i3i3ii−i−iii−i−i000000000000
χ382-22-22-2-22-22-22-1-11-111-1-1111-11-1-1122-2-20000−2i−2i2i2i0000-111-1−3−333−33−33−i3−i3i3i3i3i3−i3−i3ii−i−iii−i−i000000000000
χ392-22-22-2-22-22-22-1-11-111-1-1111-11-1-11-2-2220000000022-2-21-1-1133−3−3−33−33-1-111-1-11133−3−3−3−333000000000000
χ402-22-22-2-22-22-22-1-11-111-1-1111-11-1-11-2-2220000000022-2-21-1-11−3−3333−33−3-1-111-1-111−3−33333−3−3000000000000
χ412-22-22-2-22-22-22-1-11-111-1-1111-11-1-11-2-22200000000-2-2221-1-1133−3−3−33−3311-1-111-1-1−3−33333−3−3000000000000
χ422-22-22-2-22-22-22-1-11-111-1-1111-11-1-11-2-22200000000-2-2221-1-11−3−3333−33−311-1-111-1-133−3−3−3−333000000000000
χ432-2-2-2-22222-2-2222-2-222-2-2-2-2-2-2222200002-2000000000000002-22-2000000000000000000002−2−222−2−220000
χ442-2-2-2-22222-2-2222-2-222-2-2-2-2-2-2222200002-2000000000000002-22-200000000000000000000−222−2−222−20000
χ452-2-2-2-22222-2-2222-2-222-2-2-2-2-2-222220000-2200000000000000-22-22000000000000000000002−2−22−222−20000
χ462-2-2-2-22222-2-2222-2-222-2-2-2-2-2-222220000-2200000000000000-22-2200000000000000000000−222−22−2−220000
χ4744444444-4-4-4-4-2-2-2-2222222-2-2-222-24-44-4000000000000-2-222000000000000000000000000000000000000
χ4844444444-4-4-4-4-2-2-2-2222222-2-2-222-2-44-4400000000000022-2-2000000000000000000000000000000000000
χ49444-4-4-44-400004-444000000-4-4-40040000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ50444-4-4-44-400004-444000000-4-4-4004000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ51444-4-4-44-40000-22-2-2−2i32i3−2i32i3−2i32i3222−2i32i3-20000000000002i−2i2i−2i0000000000002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ2200000000000000000000
χ52444-4-4-44-40000-22-2-2−2i32i3−2i32i3−2i32i3222−2i32i3-2000000000000−2i2i−2i2i000000000000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ2200000000000000000000
χ53444-4-4-44-40000-22-2-22i3−2i32i3−2i32i3−2i32222i3−2i3-20000000000002i−2i2i−2i0000000000002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ1400000000000000000000
χ54444-4-4-44-40000-22-2-22i3−2i32i3−2i32i3−2i32222i3−2i3-2000000000000−2i2i−2i2i000000000000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ1400000000000000000000
χ5544-44-4-4-4444-4-4-2-2-22-2-2-2-222-2222220000004-40000000000000000-2-2220000000000000000000000000000
χ5644-44-4-4-4444-4-4-2-2-22-2-2-2-222-222222000000-44000000000000000022-2-20000000000000000000000000000
χ5744-44-4-4-44-4-444444-4-4-4-4-4444-4-444-400000000000000000000000000000000000000000000000000000000
χ5844-44-4-4-44-4-444-2-2-222222-2-2-222-2-220000000000000000000023−23−232300000000000000000000000000000000
χ5944-44-4-4-44-4-444-2-2-222222-2-2-222-2-2200000000000000000000−232323−2300000000000000000000000000000000
χ6044-4-444-4-400004-44-4000000-44400-4000000002i−2i2i−2i0000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ6144-4-444-4-400004-44-4000000-44400-400000000−2i2i−2i2i000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ6244-4-444-4-40000-22-22−2i32i3−2i32i32i3−2i32-2-22i3−2i32000000002i−2i2i−2i0000000000000000000000002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ14000000000000
χ6344-4-444-4-40000-22-22−2i32i3−2i32i32i3−2i32-2-22i3−2i3200000000−2i2i−2i2i000000000000000000000000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14000000000000
χ6444-4-444-4-40000-22-222i3−2i32i3−2i3−2i32i32-2-2−2i32i32000000002i−2i2i−2i0000000000000000000000002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ22000000000000
χ6544-4-444-4-40000-22-222i3−2i32i3−2i3−2i32i32-2-2−2i32i3200000000−2i2i−2i2i000000000000000000000000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22000000000000
χ664-444-44-4-400004-4-440000004-4400-40000000000002i−2i−2i2i0000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ674-444-44-4-400004-4-440000004-4400-4000000000000−2i2i2i−2i000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ684-444-44-4-40000-222-2−2i32i32i3−2i3−2i32i3-22-22i3−2i320000000000002i−2i−2i2i0000000000002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ1400000000000000000000
χ694-444-44-4-40000-222-2−2i32i32i3−2i3−2i32i3-22-22i3−2i32000000000000−2i2i2i−2i000000000000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ1400000000000000000000
χ704-444-44-4-40000-222-22i3−2i3−2i32i32i3−2i3-22-2−2i32i320000000000002i−2i−2i2i0000000000002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ2200000000000000000000
χ714-444-44-4-40000-222-22i3−2i3−2i32i32i3−2i3-22-2−2i32i32000000000000−2i2i2i−2i000000000000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ2200000000000000000000
χ724-44-44-4-444-44-4-2-22-2-2-222-2-22-222224-4-44000000000000-22-22000000000000000000000000000000000000
χ734-44-44-4-444-44-4-2-22-2-2-222-2-22-22222-444-40000000000002-22-2000000000000000000000000000000000000
χ744-4-444-44-400004-4-4-400000044-4004000000002-2-220000000000000000000000002-2-222-2-22000000000000
χ754-4-444-44-400004-4-4-400000044-400400000000-222-2000000000000000000000000-222-2-222-2000000000000
χ764-4-444-44-40000-2222−2i32i32i3−2i32i3−2i3-2-22−2i32i3-2000000002-2-22000000000000000000000000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3000000000000
χ774-4-444-44-40000-2222−2i32i32i3−2i32i3−2i3-2-22−2i32i3-200000000-222-20000000000000000000000001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3000000000000
χ784-4-444-44-40000-22222i3−2i3−2i32i3−2i32i3-2-222i3−2i3-2000000002-2-22000000000000000000000000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3000000000000
χ794-4-444-44-40000-22222i3−2i3−2i32i3−2i32i3-2-222i3−2i3-200000000-222-20000000000000000000000001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3000000000000
χ804-4-4-4-44444-4-44-2-222-2-2222222-2-2-2-200004-400000000000000-22-2200000000000000000000000000000000
χ814-4-4-4-44444-4-44-2-222-2-2222222-2-2-2-20000-44000000000000002-22-200000000000000000000000000000000
χ824-4-4-4-4444-444-444-4-4-4-44444-4-44-4-4400000000000000000000000000000000000000000000000000000000
χ834-4-4-4-4444-444-4-2-22222-2-2-2-222-222-200000000000000000000000023−23−23230000000000000000000000000000
χ844-4-4-4-4444-444-4-2-22222-2-2-2-222-222-2000000000000000000000000−232323−230000000000000000000000000000

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