Finite Group Databasebeta

← Group #72271924

Character table — Group #72271924

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222444444444444444448888888888888888888812121212161616161616161616161616161616161616161616242424242424242424242424242432323232323296969696
order12222362222444444666121212122224444444666612121212121222222444666661212121212121212121212122222444444444488242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-111111111111-1-11-1-1-1-1-1111111-1-1-1-1111111-1-111-111-111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-111-1-1
χ61111111111111-1-111111111111-1-11-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-111-1-111
χ71111111111111-1-111111111111-1-11-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-111-111-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111
χ81111111111111-1-111111111111-1-11-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-1
χ911111111111-1-111111111111-1-1-1-1-1111-1-11111-1-1111111-1-11111-1-1-111-1111111-111-1-11-11-11-111-1-111-1-1-1-1-1-1-1-11-11-1
χ1011111111111-1-111111111111-1-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-111-1-111-1-1111111-11-11
χ1111111111111-1-111111111111-1-1-1-1-1111-1-11111-1-11111-1-1111111-1-1-111-1111111-111-1-1-11-11-11-1-111-1-111-1-1-1-1-1-1-11-11
χ1211111111111-1-111111111111-1-1-1-1-1111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-1-111-1-1111111111-11-1
χ1311111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1111-1-11-1111-1-1-1-111-11-1-1111-1-11
χ1411111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-11-1-11-1-11111-1-1-1111-1-11-1111-1-1-1-1111-111-1-1-111-1
χ1511111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-111-11-1-1-11111-1-1-11-1-111-111-1
χ1611111111111-1-1-1-1111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11-1-11111-1-1-111-111-11-1-1-11111-1-11-111-1-11-1-11
χ17222222222-2-20022-2-2222-2-2-2-2000002-2-20022-2-20022-2-20022000000000000000002-200020-20-200-2-200220000000000
χ18222222222-2-20022-2-2222-2-2-2-2000002-2-20022-2-20022-2-200-2-2000000000000000002-2000-20202002200-2-20000000000
χ19222222222-2-200-2-2-2-2222-2-2-2-200000-2220022-2-200-2-222002200000000000000000-220002020200-2-200-2-20000000000
χ20222222222-2-200-2-2-2-2222-2-2-2-200000-2220022-2-200-2-22200-2-200000000000000000-22000-20-20-2002200220000000000
χ212222222-2-2220022-2-2222-2-2-2-200000-22-200-2-2220022-2-2220000000000000000000-220020-20-20-2-20022000000000000
χ222222222-2-2220022-2-2222-2-2-2-200000-22-200-2-2220022-2-2-2-20000000000000000000-2200-2020202200-2-2000000000000
χ232222222-2-22200-2-2-2-2222-2-2-2-2000002-2200-2-22200-2-2222200000000000000000002-200202020-2-200-2-2000000000000
χ242222222-2-22200-2-2-2-2222-2-2-2-2000002-2200-2-22200-2-222-2-200000000000000000002-200-20-20-20220022000000000000
χ252222222-2-2-2-22222222222222-2-2222-2-22-2-2-2-2-2-222222200000000-2-220020000002-2-2-2-2000000000000000000000000
χ262222222-2-2-2-222-2-2222222222-2-2-2-2222-222-2-2-2-222-2-2-2-200000000-2-2-200-200000022222000000000000000000000000
χ272222222-2-2-2-2-2-22222222222222-2-2-2-2-2222-2-2-2-2-2-222220000000022-200-2000000-2-2-222000000000000000000000000
χ282222222-2-2-2-2-2-2-2-22222222222222-222-2-2-2-2-2-2-2-2-2-2-2-2-200000000222002000000-222-2-2000000000000000000000000
χ2922222-1-12222222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000022-1-1-1-10000
χ3022222-1-12222222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-1-1-111-1111111-1-1-1-1-100000000000000-2-211110000
χ3122222-1-1222222-2-222-1-1-1-1-1-1-122-2-22-2-2-2-2-2-1-1-1-1-1-11111000022-2-2-1-11-1-11-1-11111-11111000000000000002-2-1-1110000
χ3222222-1-1222222-2-222-1-1-1-1-1-1-122-2-22-2-2-2-2-2-1-1-1-1-1-111110000-2-222-1-1111111-1-1-1-1-1111100000000000000-2211-1-10000
χ3322222-1-12222-2-22222-1-1-1-1-1-1-1-2-2-2-2-2222-2-2-1-1-1-111-1-1-1-100002222111-1-11-1-1-1-1-1-11-1-11100000000000000-2-211110000
χ3422222-1-12222-2-22222-1-1-1-1-1-1-1-2-2-2-2-2222-2-2-1-1-1-111-1-1-1-10000-2-2-2-21111111111111-1-1110000000000000022-1-1-1-10000
χ3522222-1-12222-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-2-222-1-1-1-1111111000022-2-211-1-1-1-1-1-11111111-1-100000000000000-2211-1-10000
χ3622222-1-12222-2-2-2-222-1-1-1-1-1-1-1-2-222-2-2-2-222-1-1-1-11111110000-2-22211-111-111-1-1-1-1111-1-1000000000000002-2-1-1110000
χ3722222-1-1-2-2-2-2222222-1-1-1-1-1-1-1-2-2222-2-22-2-21111-1-1-1-1-1-10000000011-1−i3i3-1−i3i3−i3−i3i3i3-111110000000000000000−i3i3−i3i30000
χ3822222-1-1-2-2-2-2222222-1-1-1-1-1-1-1-2-2222-2-22-2-21111-1-1-1-1-1-10000000011-1i3−i3-1i3−i3i3i3−i3−i3-111110000000000000000i3−i3i3−i30000
χ3922222-1-1-2-2-2-222-2-222-1-1-1-1-1-1-1-2-2-2-2222-2221111-1-1111100000000111−i3i31−i3i3i3i3−i3−i3-1-1-1-1-10000000000000000−i3i3i3−i30000
χ4022222-1-1-2-2-2-222-2-222-1-1-1-1-1-1-1-2-2-2-2222-2221111-1-1111100000000111i3−i31i3−i3−i3−i3i3i3-1-1-1-1-10000000000000000i3−i3−i3i30000
χ4122222-1-1-2-2-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-2222111111-1-1-1-100000000-1-11−i3i31−i3i3−i3−i3i3i3111-1-10000000000000000i3−i3i3−i30000
χ4222222-1-1-2-2-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-2222111111-1-1-1-100000000-1-11i3−i31i3−i3i3i3−i3−i3111-1-10000000000000000−i3i3−i3i30000
χ4322222-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12222-222-2-2-2111111111100000000-1-1-1−i3i3-1−i3i3i3i3−i3−i31-1-1110000000000000000i3−i3−i3i30000
χ4422222-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-12222-222-2-2-2111111111100000000-1-1-1i3−i3-1i3−i3−i3−i3i3i31-1-1110000000000000000−i3i3i3−i30000
χ4522-2-22222-22-200002-2-2-2222-2-2002-200002-22-22-20000000022000000200-20000000002-20-220-20002-22-2000000000000
χ4622-2-22222-22-200002-2-2-2222-2-2002-200002-22-22-200000000-2-2000000200-20000000002-202-202000-22-22000000000000
χ4722-2-22222-22-200002-2-2-2222-2-200-220000-222-22-20000000022000000-2002000000000-220-2-2020002-2-22000000000000
χ4822-2-22222-22-200002-2-2-2222-2-200-220000-222-22-200000000-2-2000000-2002000000000-220220-2000-222-2000000000000
χ4922-2-22222-2-222200-22-2-22-2-2222-200-2000002-2-22220000222200002-20000000000-20000-2-200002-2-2200000000000000
χ5022-2-22222-2-222200-22-2-22-2-2222-200-2000002-2-22220000-2-2-2-200002-20000000000-20000220000-222-200000000000000
χ5122-2-22222-2-22-2-200-22-2-22-2-222-22002000002-2-22-2-2000022-2-20000-22000000000020000-2200002-22-200000000000000
χ5222-2-22222-2-22-2-200-22-2-22-2-222-22002000002-2-22-2-20000-2-2220000-220000000000200002-20000-22-2200000000000000
χ5322-2-2222-222-22200-22-2-22-2-222-2200-200000-222-222000000000000-220000000000-200000022-2-20000-222-20000000000
χ5422-2-2222-222-22200-22-2-22-2-222-2200-200000-222-222000000000000-220000000000-2000000-2-22200002-2-220000000000
χ5522-2-2222-222-2-2-200-22-2-22-2-2222-200200000-222-2-2-20000000000002-2000000000020000002-2-220000-22-220000000000
χ5622-2-2222-222-2-2-200-22-2-22-2-2222-200200000-222-2-2-20000000000002-200000000002000000-222-200002-22-20000000000
χ5722-2-2222-22-2200002-2-2-2222-2-2002-20000-22-22-220000002200000000200-2000000000-22-20020-2-220000-220000000000
χ5822-2-2222-22-2200002-2-2-2222-2-2002-20000-22-22-22000000-2-200000000200-2000000000-22200-2022-200002-20000000000
χ5922-2-2222-22-2200002-2-2-2222-2-200-2200002-2-22-220000002200000000-20020000000002-2-200-202-2200002-20000000000
χ6022-2-2222-22-2200002-2-2-2222-2-200-2200002-2-22-22000000-2-200000000-20020000000002-220020-22-20000-220000000000
χ6144444-2-244-4-40044-4-4-2-2-22222000004-4-400-2-22200-2-222000000000000000000000-2200000000000000000000000000
χ6244444-2-244-4-400-4-4-4-4-2-2-2222200000-44400-2-2220022-2-20000000000000000000002-200000000000000000000000000
χ6344444-2-2-4-4440044-4-4-2-2-2222200000-44-40022-2-200-2-2220000000000000000000002-200000000000000000000000000
χ6444444-2-2-4-44400-4-4-4-4-2-2-22222000004-440022-2-20022-2-2000000000000000000000-2200000000000000000000000000
χ65444-4-4440000004i−4i004-4-4000000000000000000004i−4i0000002-22i−2i000220-2-22i−2i2i−2i00000000000000000000000000000
χ66444-4-4440000004i−4i004-4-4000000000000000000004i−4i000000-22−2i2i000-2-2022−2i2i−2i2i00000000000000000000000000000
χ67444-4-444000000−4i4i004-4-400000000000000000000−4i4i0000002-2−2i2i000220-2-2−2i2i−2i2i00000000000000000000000000000
χ68444-4-444000000−4i4i004-4-400000000000000000000−4i4i000000-222i−2i000-2-20222i−2i2i−2i00000000000000000000000000000
χ69444-4-4-2-20000004i−4i00-222−2i32i3−2i32i30000000000000000−2i2i23−2300002-22i−2i000−1−i3−1+i301+i31−i32ζ11−2ζ112ζ7−2ζ700000000000000000000000000000
χ70444-4-4-2-20000004i−4i00-222−2i32i3−2i32i30000000000000000−2i2i23−230000-22−2i2i0001+i31−i30−1−i3−1+i3−2ζ112ζ11−2ζ72ζ700000000000000000000000000000
χ71444-4-4-2-20000004i−4i00-2222i3−2i32i3−2i30000000000000000−2i2i−232300002-22i−2i000−1+i3−1−i301−i31+i32ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000
χ72444-4-4-2-20000004i−4i00-2222i3−2i32i3−2i30000000000000000−2i2i−23230000-22−2i2i0001−i31+i30−1+i3−1−i3−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000
χ73444-4-4-2-2000000−4i4i00-222−2i32i3−2i32i300000000000000002i−2i−232300002-2−2i2i000−1−i3−1+i301+i31−i3−2ζ112ζ11−2ζ72ζ700000000000000000000000000000
χ74444-4-4-2-2000000−4i4i00-222−2i32i3−2i32i300000000000000002i−2i−23230000-222i−2i0001+i31−i30−1−i3−1+i32ζ11−2ζ112ζ7−2ζ700000000000000000000000000000
χ75444-4-4-2-2000000−4i4i00-2222i3−2i32i3−2i300000000000000002i−2i23−2300002-2−2i2i000−1+i3−1−i301−i31+i3−2ζ72ζ7−2ζ112ζ1100000000000000000000000000000
χ76444-4-4-2-2000000−4i4i00-2222i3−2i32i3−2i300000000000000002i−2i23−230000-222i−2i0001−i31+i30−1+i3−1−i32ζ7−2ζ72ζ11−2ζ1100000000000000000000000000000
χ7744-4-44-2-24-44-400004-422-2-2-222004-400004-4-22-220000000000000000-2002000000000-22000000000000000000000000
χ7844-4-44-2-24-44-400004-422-2-2-22200-440000-44-22-220000000000000000200-20000000002-2000000000000000000000000
χ7944-4-44-2-24-4-444400-4422-222-2-24-400-400000-222-2-2-2000000000000-22000000000020000000000000000000000000000
χ8044-4-44-2-24-4-44-4-400-4422-222-2-2-4400400000-222-2220000000000002-20000000000-20000000000000000000000000000
χ8144-4-44-2-2-444-44400-4422-222-2-2-4400-4000002-2-22-2-20000000000002-2000000000020000000000000000000000000000
χ8244-4-44-2-2-444-4-4-400-4422-222-2-24-4004000002-2-2222000000000000-220000000000-20000000000000000000000000000
χ8344-4-44-2-2-44-4400004-422-2-2-222004-40000-442-22-20000000000000000-20020000000002-2000000000000000000000000
χ8444-4-44-2-2-44-4400004-422-2-2-22200-4400004-42-22-20000000000000000200-2000000000-22000000000000000000000000
χ8588-88-8880000000000-88-80000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-88-8-4-400000000004-44−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000000
χ8788-88-8-4-400000000004-444i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000000
χ888-80008-800004-400000000000000000000000004-400004-44-4000000000000000000000000000000000000000000000
χ898-80008-800004-400000000000000000000000004-40000-44-44000000000000000000000000000000000000000000000
χ908-80008-80000-440000000000000000000000000-4400004-4-44000000000000000000000000000000000000000000000
χ918-80008-80000-440000000000000000000000000-440000-444-4000000000000000000000000000000000000000000000
χ9216-16000-8800008-80000000000000000000000000-4400000000000000000000000000000000000000000000000000000
χ9316-16000-880000-8800000000000000000000000004-400000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.