Finite Group Databasebeta

← Group #13140181

Character table — Group #13140181

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636727272727272
order1222223446664661212121233666666666612121212366666666612121212121212121212121212122222666666668888242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1-1111111-1-1-111-1-1111111-1-1-1-11111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ61111-1-1111111-1-1-111-1-1111111-1-1-1-11111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ71111-1-1111111-1-1-111-1-1111111-1-1-1-11111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-11-1-111
χ81111-1-1111111-1-1-111-1-1111111-1-1-1-11111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111-111-1-1
χ922222222222222222222-122-1-1-1-1-1-12-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000
χ1022222222222222222222-122-1-1-1-1-1-12-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000000000
χ112222222222222222222-12-1-1222222-12-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-1000000
χ122222222222222222222-12-1-1222222-12-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000000000000-2-2-2-211111111000000
χ132222222-2-2222-222-2-2-2-2222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
χ142222222-2-2222-222-2-2-2-22-122-1-1-1-1-1-12-1-2-2-2-2-122-1-1-1-1-1-1-111-2-211111111110000−i3−i3i3i3−i3−i3i3i3000000000000000000
χ152222222-2-2222-222-2-2-2-22-122-1-1-1-1-1-12-1-2-2-2-2-122-1-1-1-1-1-1-111-2-211111111110000i3i3−i3−i3i3i3−i3−i3000000000000000000
χ162222222-2-2222-222-2-2-2-2-12-1-1222222-121111-1-1-1-1-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−3000000
χ172222222-2-2222-222-2-2-2-2-12-1-1222222-121111-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−333000000
χ182222-2-2222222-2-2-222-2-22-122-1-111112-12222-1-2-2-1-11111-1-1-1-2-211-1-1-1-1111122-2-2-1-1-1-11111000000000000000000
χ192222-2-2222222-2-2-222-2-22-122-1-111112-12222-1-2-2-1-11111-1-1-1-2-211-1-1-1-11111-2-2221111-1-1-1-1000000000000000000
χ202222-2-2222222-2-2-222-2-2-12-1-122-2-2-2-2-12-1-1-1-1-111-1-11111-12211-2-2-1-1-1-1111100000000000022-2-2-1-1-1-11111000000
χ212222-2-2222222-2-2-222-2-2-12-1-122-2-2-2-2-12-1-1-1-1-111-1-11111-12211-2-2-1-1-1-11111000000000000-2-2221111-1-1-1-1000000
χ222222-2-22-2-22222-2-2-2-222222222-2-2-2-222-2-2-2-22-2-222-2-2-2-22-2-22222-2-2-2-22222000000000000000000000000000000
χ232222-2-22-2-22222-2-2-2-2222-122-1-111112-1-2-2-2-2-1-2-2-1-11111-11122-1-11111-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000000000
χ242222-2-22-2-22222-2-2-2-2222-122-1-111112-1-2-2-2-2-1-2-2-1-11111-11122-1-11111-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000000000
χ252222-2-22-2-22222-2-2-2-222-12-1-122-2-2-2-2-121111-111-1-11111-1-2-2-1-1221111-1-1-1-1000000000000000033−3−3−3−333000000
χ262222-2-22-2-22222-2-2-2-222-12-1-122-2-2-2-2-121111-111-1-11111-1-2-2-1-1221111-1-1-1-10000000000000000−3−33333−3−3000000
χ272-22-20022-2-22-20002-20022-2-2-2-200002222-2-2200-2-2000022-2000022-2-20000002-200002-22-2000000000000000000
χ282-22-20022-2-22-20002-20022-2-2-2-200002222-2-2200-2-2000022-2000022-2-2000000-220000-22-22000000000000000000
χ292-22-20022-2-22-20002-2002-1-2-211−i3−i3i3i32-122-2-2-10011−i3−i3i3i3-1-1100−i3i3-1-111−i3−i3i3i3002-2−i3i3−i3i3-11-11000000000000000000
χ302-22-20022-2-22-20002-2002-1-2-211−i3−i3i3i32-122-2-2-10011−i3−i3i3i3-1-1100−i3i3-1-111−i3−i3i3i300-22i3−i3i3−i31-11-1000000000000000000
χ312-22-20022-2-22-20002-2002-1-2-211i3i3−i3−i32-122-2-2-10011i3i3−i3−i3-1-1100i3−i3-1-111i3i3−i3−i3002-2i3−i3i3−i3-11-11000000000000000000
χ322-22-20022-2-22-20002-2002-1-2-211i3i3−i3−i32-122-2-2-10011i3i3−i3−i3-1-1100i3−i3-1-111i3i3−i3−i300-22−i3i3−i3i31-11-1000000000000000000
χ332-22-2002-22-22-2000-220022-2-2-2-2000022-2-222200-2-200002-220000-2-22200002-2002-2-220000000000000000000000
χ342-22-2002-22-22-2000-220022-2-2-2-2000022-2-222200-2-200002-220000-2-2220000-2200-222-20000000000000000000000
χ352-22-2002-22-22-2000-22002-1-2-211−i3−i3i3i32-1-2-222-10011−i3−i3i3i3-11-100i3−i311-1-1i3i3−i3−i32-200-111-1−i3i3i3−i3000000000000000000
χ362-22-2002-22-22-2000-22002-1-2-211−i3−i3i3i32-1-2-222-10011−i3−i3i3i3-11-100i3−i311-1-1i3i3−i3−i3-22001-1-11i3−i3−i3i3000000000000000000
χ372-22-2002-22-22-2000-22002-1-2-211i3i3−i3−i32-1-2-222-10011i3i3−i3−i3-11-100−i3i311-1-1−i3−i3i3i32-200-111-1i3−i3−i3i3000000000000000000
χ382-22-2002-22-22-2000-22002-1-2-211i3i3−i3−i32-1-2-222-10011i3i3−i3−i3-11-100−i3i311-1-1−i3−i3i3i3-22001-1-11−i3i3i3−i3000000000000000000
χ392-2-222-2200-2-2202-20000222-22-22-22-2-2-2000022-22-22-22-2-2000000000000000000000000002−22−22−22−22−22−2000000
χ402-2-222-2200-2-2202-20000222-22-22-22-2-2-2000022-22-22-22-2-200000000000000000000000000−22−22−22−22−22−22000000
χ412-2-222-2200-2-2202-20000-12-112-22-22-21-23−33−3-1-11-11-11-111003−3003−33−33−33−30000000000002−22−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ422-2-222-2200-2-2202-20000-12-112-22-22-21-23−33−3-1-11-11-11-111003−3003−33−33−33−3000000000000−22−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ432-2-222-2200-2-2202-20000-12-112-22-22-21-2−33−33-1-11-11-11-11100−3300−33−33−33−330000000000002−22−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ442-2-222-2200-2-2202-20000-12-112-22-22-21-2−33−33-1-11-11-11-11100−3300−33−33−33−33000000000000−22−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ452-2-22-22200-2-220-220000222-22-2-22-22-2-200002-222-2-22-22-2000000000000000000000000002−2−222−22−2−22−22000000
χ462-2-22-22200-2-220-220000222-22-2-22-22-2-200002-222-2-22-22-200000000000000000000000000−222−2−22−222−22−2000000
χ472-2-22-22200-2-220-220000-12-112-2-22-221-23−33−3-11-1-111-11-1100−33003−33−3−33−330000000000002−2−22ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ482-2-22-22200-2-220-220000-12-112-2-22-221-23−33−3-11-1-111-11-1100−33003−33−3−33−33000000000000−222−2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ492-2-22-22200-2-220-220000-12-112-2-22-221-2−33−33-11-1-111-11-11003−300−33−333−33−30000000000002−2−22ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ502-2-22-22200-2-220-220000-12-112-2-22-221-2−33−33-11-1-111-11-11003−300−33−333−33−3000000000000−222−2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ514444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000
χ524444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ534444-4-4444444-4-4-444-4-4-2-2-2-2-2-22222-2-2-2-2-2-212211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000
χ544444-4-44-4-44444-4-4-4-444-2-2-2-2-2-22222-2-2222212211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ5544-4-4004004-4-4000000044-44-440000-4-40000400-440000-400000000000000000000000000000000000000000000
χ5644-4-4004004-4-400000004-2-442-2−2i32i32i3−2i3-420000-2002-2−2i32i32i3−2i3200000000000000000000000000000000000000000000
χ5744-4-4004004-4-400000004-2-442-22i3−2i3−2i32i3-420000-2002-22i3−2i3−2i32i3200000000000000000000000000000000000000000000
χ5844-4-4004004-4-40000000-242-2-4400002-423−23−2323-2002-20000200000023−23−23230000000000000000000000000000000000
χ5944-4-4004004-4-40000000-242-2-4400002-4−232323−23-2002-200002000000−232323−230000000000000000000000000000000000
χ6044-4-4004004-4-40000000-2-22-22-2−2i32i32i3−2i32223−23−2323100-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i000000000000000000000000000000
χ6144-4-4004004-4-40000000-2-22-22-2−2i32i32i3−2i322−232323−23100-11i3−i3−i3i3-10000003−3−333i−3i−3i3i000000000000000000000000000000
χ6244-4-4004004-4-40000000-2-22-22-22i3−2i3−2i32i32223−23−2323100-11−i3i3i3−i3-1000000−333−33i−3i−3i3i000000000000000000000000000000
χ6344-4-4004004-4-40000000-2-22-22-22i3−2i3−2i32i322−232323−23100-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i000000000000000000000000000000
χ644-44-40044-4-44-40004-400-2422-4-40000-24-2-222-200220000-24-40000-2-2220000000000000000000000000000000000
χ654-44-40044-4-44-40004-400-2-22222−2i3−2i32i32i3-2-2-2-222100-1-1i3i3−i3−i31-2200−2i32i311-1-1i3i3−i3−i3000000000000000000000000000000
χ664-44-40044-4-44-40004-400-2-222222i32i3−2i3−2i3-2-2-2-222100-1-1−i3−i3i3i31-22002i3−2i311-1-1−i3−i3i3i3000000000000000000000000000000
χ674-44-4004-44-44-4000-4400-2422-4-40000-2422-2-2-200220000-2-44000022-2-20000000000000000000000000000000000
χ684-44-4004-44-44-4000-4400-2-22222−2i3−2i32i32i3-2-222-2-2100-1-1i3i3−i3−i312-2002i3−2i3-1-111−i3−i3i3i3000000000000000000000000000000
χ694-44-4004-44-44-4000-4400-2-222222i32i3−2i3−2i3-2-222-2-2100-1-1−i3−i3i3i312-200−2i32i3-1-111i3i3−i3−i3000000000000000000000000000000
χ704-4-444-4400-4-4404-400004-24-4-22-22-22-420000-24-4-22-22-22200000000000000000000000000000000000000000000
χ714-4-444-4400-4-4404-40000-2-2-22-22-22-222223−2323−231-221-11-11-1-10023−2300−33−33−33−33000000000000000000000000000000
χ724-4-444-4400-4-4404-40000-2-2-22-22-22-2222−2323−23231-221-11-11-1-100−2323003−33−33−33−3000000000000000000000000000000
χ734-4-44-44400-4-440-4400004-24-4-222-22-2-420000-2-44-222-22-2200000000000000000000000000000000000000000000
χ744-4-44-44400-4-440-440000-2-2-22-222-22-22223−2323−2312-21-1-11-11-100−232300−33−333−33−3000000000000000000000000000000
χ754-4-44-44400-4-440-440000-2-2-22-222-22-222−2323−232312-21-1-11-11-10023−23003−33−3−33−33000000000000000000000000000000
χ76666666-366-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000000000000000022-1-1-1-1
χ77666666-366-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000000000000000000-2-21111
χ78666666-3-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3
χ79666666-3-6-6-3-3-3-6-3-33333000000000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3
χ806666-6-6-366-3-3-3-633-3-33300000000000000000000000000000000000000000000000000000000000000002-2-1-111
χ816666-6-6-366-3-3-3-633-3-3330000000000000000000000000000000000000000000000000000000000000000-2211-1-1
χ826666-6-6-3-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3
χ836666-6-6-3-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3
χ841212-12-1200-600-6660000063−630000000000000000000000000000000000000000000000000000000000000000000000
χ851212-12-1200-600-66600000−63630000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-1200-612-126-66000-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8712-1212-1200-6-12126-660006-6000000000000000000000000000000000000000000000000000000000000000000000000
χ8812-12-121212-12-60066-60-6600000000000000000000000000000000000000000000000000000000000000000000000000
χ8912-12-1212-1212-60066-606-600000000000000000000000000000000000000000000000000000000000000000000000000

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