Finite Group Databasebeta

← Group #72271910

Character table — Group #72271910

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222444444444444444448888888888888888888812121212161616161616161616161616161616161616161616242424242424242424242424242432323232323296969696
order12222362222224444666666622444444446666121212121212224424446666121212121212121212121212122222244444444444121212124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-11111111111-1-111-1-1-1-1-1111111-1-1-1-1111111-1-11-111-111-1-1-1-111-1-1-1-1111-1-1-1-1111-1-1-1-11-111-1-11-11-1
χ61111111111111-1-11111111111-1-111-1-1-1-1-1111111-1-1-1-11111-1-1111-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1111-1-1-1-1-11-1-111-11-11
χ71111111111111-1-11111111111-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11-111-111-1-1-1-111-1-1-1-1-1-1-11111-1-1-111111-111-1-1-11-11
χ81111111111111-1-11111111111-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-11111-11-1-1111-11-1
χ91111111-1-1111111111111111-1-1-1-1-1111-1-111-1-111111111-1-11111-1-111-1111111-1-111-1-11-1-11-11-111-111-1-1-1-1-1-1-1-111-1-1
χ101111111-1-1111111111111111-1-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11-11-111-111-1-1111111-1-111
χ111111111-1-1111111111111111-1-1-1-1-1111-1-111-1-1111111-1-1111111-1-111-1111111-1-111-1-1-111-11-11-1-11-1-111-1-1-1-1-1-1-1-111
χ121111111-1-1111111111111111-1-1-1-1-1111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11-11-1-11-1-11111111111-1-1
χ131111111-1-11111-1-1111111111-111-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-11-1111-1-1-111-11-1-1111-1-11
χ141111111-1-11111-1-1111111111-111-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-111-11-1-11-1-11111-1-1-1-1111-1-1-11-1111-1-1-1111-111-1-1-111-1
χ151111111-1-11111-1-1111111111-111-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-111-1111-11-1-1-1111-1-1-11-1-111-111-1
χ161111111-1-11111-1-1111111111-111-1-1-1-1-11111-1-111-1-1-1-1-1-111-1-111-11-1-11-1-11111-1-1-1-111-1111-11-1-1-1111-1-11-111-1-11-1-11
χ17222222200-2-22222-2-22-2-2-2-222000002-2-2002200-2-222-2-22200000000000000000002-200200-20-20-2-2022000000000000
χ18222222200-2-22222-2-22-2-2-2-222000002-2-2002200-2-222-2-2-2-200000000000000000002-200-2002020220-2-2000000000000
χ19222222200-2-222-2-2-2-22-2-2-2-22200000-222002200-2-2-2-222220000000000000000000-22002002020-2-20-2-2000000000000
χ20222222200-2-222-2-2-2-22-2-2-2-22200000-222002200-2-2-2-222-2-20000000000000000000-2200-200-20-2022022000000000000
χ21222222200-2-2-2-222222-2-2-2-22200000-22-200-2-2002222-2-2002200000000000000000-22000-2-2020200200-2-20000000000
χ22222222200-2-2-2-222222-2-2-2-22200000-22-200-2-2002222-2-200-2-200000000000000000-22000220-20-200-200220000000000
χ23222222200-2-2-2-2-2-2222-2-2-2-222000002-2200-2-20022-2-2220022000000000000000002-2000-2-20-20-200200220000000000
χ24222222200-2-2-2-2-2-2222-2-2-2-222000002-2200-2-20022-2-22200-2-2000000000000000002-200022020200-200-2-20000000000
χ2522222222222-2-222-2-222222222-2-2-2-2-2-2222-2-222-2-22222000000002-200-2000000-2-2-2-222000000000000000000000000
χ2622222222222-2-2-2-2-2-22222222222-2-222-2-2-2-2-222-2-2-2-2-2-20000000022002000000-2-222-2-2000000000000000000000000
χ272222222-2-222-2-222-2-22222222-22222-2-22-2-2-2-2-2-2-2-2222200000000-2200200000022-2-2-2-2000000000000000000000000
χ282222222-2-222-2-2-2-2-2-22222222-2-2-22222-222-2-2-2-2-2-2-2-2-2-200000000-2-200-2000000222222000000000000000000000000
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
χ3022222-1-12222222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-1-111-1111111-1-1-1-1-1-100000000000000-2-211110000
χ3122222-1-1222222-2-222-1-1-1-1-1-1-12-2-222-2-2-2-2-2-1-1-1-1-1-11111000022-2-2-11-1-11-1-11111-1-11111000000000000002-2-1-1110000
χ3222222-1-1222222-2-222-1-1-1-1-1-1-12-2-222-2-2-2-2-2-1-1-1-1-1-111110000-2-222-1111111-1-1-1-1-1-1111100000000000000-2211-1-10000
χ3322222-1-12222-2-222-2-2-1-1-1-1-1-1-12-2-2-2-2-2-222211-1-111-1-1-1-100000000-11−i3i31−i3i3−i3−i3i3i31111-1-10000000000000000−i3i3−i3i30000
χ3422222-1-12222-2-222-2-2-1-1-1-1-1-1-12-2-2-2-2-2-222211-1-111-1-1-1-100000000-11i3−i31i3−i3i3i3−i3−i31111-1-10000000000000000i3−i3i3−i30000
χ3522222-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1222-2-222-2-2-211-1-111111100000000-1-1−i3i3-1−i3i3i3i3−i3−i311-1-1110000000000000000−i3i3i3−i30000
χ3622222-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-1222-2-222-2-2-211-1-111111100000000-1-1i3−i3-1i3−i3−i3−i3i3i311-1-1110000000000000000i3−i3−i3i30000
χ3722222-1-1-2-222222222-1-1-1-1-1-1-1-2-2-2-2-2222-2-2-1-111-1-1-1-1-1-10000222211-1-11-1-1-1-1-1-111-1-11100000000000000-2-211110000
χ3822222-1-1-2-222222222-1-1-1-1-1-1-1-2-2-2-2-2222-2-2-1-111-1-1-1-1-1-10000-2-2-2-21111111111111-1-1110000000000000022-1-1-1-10000
χ3922222-1-1-2-22222-2-222-1-1-1-1-1-1-1-222-2-2-2-2-222-1-111-1-11111000022-2-21-1-1-1-1-1-111111111-1-100000000000000-2211-1-10000
χ4022222-1-1-2-22222-2-222-1-1-1-1-1-1-1-222-2-2-2-2-222-1-111-1-111110000-2-2221-111-111-1-1-1-11111-1-1000000000000002-2-1-1110000
χ4122222-1-1-2-222-2-222-2-2-1-1-1-1-1-1-1-22222-2-22-2-2111111-1-1-1-1000000001-1−i3i3-1−i3i3−i3−i3i3i3-1-111110000000000000000i3−i3i3−i30000
χ4222222-1-1-2-222-2-222-2-2-1-1-1-1-1-1-1-22222-2-22-2-2111111-1-1-1-1000000001-1i3−i3-1i3−i3i3i3−i3−i3-1-111110000000000000000−i3i3−i3i30000
χ4322222-1-1-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-22211111111110000000011−i3i31−i3i3i3i3−i3−i3-1-1-1-1-1-10000000000000000i3−i3−i3i30000
χ4422222-1-1-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-2-2-22222-22211111111110000000011i3−i31i3−i3−i3−i3i3i3-1-1-1-1-1-10000000000000000−i3i3i3−i30000
χ4522-2-2222002-22-2002-2-222-2-2-2202-2000002-22-2002-20000002200000200-200000000002-202-220-2000-22-2000000000000
χ4622-2-2222002-22-2002-2-222-2-2-2202-2000002-22-2002-2000000-2-200000200-200000000002-20-22-2020002-22000000000000
χ4722-2-2222002-22-2002-2-222-2-2-220-2200000-222-2002-20000002200000-20020000000000-2202-2-202000-2-22000000000000
χ4822-2-2222002-22-2002-2-222-2-2-220-2200000-222-2002-2000000-2-200000-20020000000000-220-2220-200022-2000000000000
χ4922-2-2222002-2-2200-22-222-2-2-2202-200000-22-2200-220000220000000200-20000000000-22-200020-22-20002-20000000000
χ5022-2-2222002-2-2200-22-222-2-2-2202-200000-22-2200-220000-2-20000000200-20000000000-222000-202-22000-220000000000
χ5122-2-2222002-2-2200-22-222-2-2-220-22000002-2-2200-220000220000000-200200000000002-2-2000-2022-2000-220000000000
χ5222-2-2222002-2-2200-22-222-2-2-220-22000002-2-2200-220000-2-20000000-200200000000002-2200020-2-220002-20000000000
χ5322-2-222222-222-200-22-2-2-222-22-2002-2000002-222-22000000000000-200000000002-2000000022-2-2000-22-220000000000
χ5422-2-222222-222-200-22-2-2-222-22-2002-2000002-222-22000000000000-200000000002-20000000-2-2220002-22-20000000000
χ5522-2-222222-22-22002-2-2-2-222-22-200-2200000-22222-2000022220000-20000000000-220000-2-220000-22-200000000000000
χ5622-2-222222-22-22002-2-2-2-222-22-200-2200000-22222-20000-2-2-2-20000-20000000000-22000022-200002-2200000000000000
χ5722-2-2222-2-2-222-200-22-2-2-222-22200-22000002-2-2-2-2200000000000020000000000-2200000002-2-22000-222-20000000000
χ5822-2-2222-2-2-222-200-22-2-2-222-22200-22000002-2-2-2-2200000000000020000000000-220000000-222-20002-2-220000000000
χ5922-2-2222-2-2-22-22002-2-2-2-222-222002-200000-22-2-22-2000022-2-20000200000000002-20000-22-20000-22200000000000000
χ6022-2-2222-2-2-22-22002-2-2-2-222-222002-200000-22-2-22-20000-2-2220000200000000002-200002-2200002-2-200000000000000
χ6144444-2-200-4-44444-4-4-22222-2-2000004-4-400-2-20022-2-222000000000000000000000-2200000000000000000000000000
χ6244444-2-200-4-444-4-4-4-4-22222-2-200000-44400-2-2002222-2-20000000000000000000002-200000000000000000000000000
χ6344444-2-200-4-4-4-44444-22222-2-200000-44-4002200-2-2-2-2220000000000000000000002-200000000000000000000000000
χ6444444-2-200-4-4-4-4-4-444-22222-2-2000004-44002200-2-222-2-2000000000000000000000-2200000000000000000000000000
χ65444-4-4440000004i−4i0040000-4-400000000000000004i−4i0000002-22i−2i00220-2-22i−2i2i−2i000000000000000000000000000000
χ66444-4-4440000004i−4i0040000-4-400000000000000004i−4i000000-22−2i2i00-2-2022−2i2i−2i2i000000000000000000000000000000
χ67444-4-444000000−4i4i0040000-4-40000000000000000−4i4i0000002-2−2i2i00220-2-2−2i2i−2i2i000000000000000000000000000000
χ68444-4-444000000−4i4i0040000-4-40000000000000000−4i4i000000-222i−2i00-2-20222i−2i2i−2i000000000000000000000000000000
χ69444-4-4-2-20000004i−4i00-2−2i32i3−2i32i3220000000000000000−2i2i23−2300002-22i−2i00−1−i3−1+i301+i31−i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ70444-4-4-2-20000004i−4i00-2−2i32i3−2i32i3220000000000000000−2i2i23−230000-22−2i2i001+i31−i30−1−i3−1+i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ71444-4-4-2-20000004i−4i00-22i3−2i32i3−2i3220000000000000000−2i2i−232300002-22i−2i00−1+i3−1−i301−i31+i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ72444-4-4-2-20000004i−4i00-22i3−2i32i3−2i3220000000000000000−2i2i−23230000-22−2i2i001−i31+i30−1+i3−1−i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ73444-4-4-2-2000000−4i4i00-2−2i32i3−2i32i32200000000000000002i−2i−232300002-2−2i2i00−1−i3−1+i301+i31−i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000000000
χ74444-4-4-2-2000000−4i4i00-2−2i32i3−2i32i32200000000000000002i−2i−23230000-222i−2i001+i31−i30−1−i3−1+i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000000000
χ75444-4-4-2-2000000−4i4i00-22i3−2i32i3−2i32200000000000000002i−2i23−2300002-2−2i2i00−1+i3−1−i301−i31+i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000000000
χ76444-4-4-2-2000000−4i4i00-22i3−2i32i3−2i32200000000000000002i−2i23−230000-222i−2i001−i31+i30−1+i3−1−i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000000000
χ7744-4-44-2-2004-44-4004-42-2-2222-204-4000004-4-2200-220000000000000-20020000000000-22000000000000000000000000
χ7844-4-44-2-2004-44-4004-42-2-2222-20-4400000-44-2200-220000000000000200-200000000002-2000000000000000000000000
χ7944-4-44-2-2004-4-4400-442-2-2222-204-400000-442-2002-20000000000000-200200000000002-2000000000000000000000000
χ8044-4-44-2-2004-4-4400-442-2-2222-20-44000004-42-2002-20000000000000200-20000000000-22000000000000000000000000
χ8144-4-44-2-244-444-400-44222-2-22-2-4004-400000-22-2-22-200000000000020000000000-220000000000000000000000000000
χ8244-4-44-2-244-44-44004-4222-2-22-2-400-44000002-2-2-2-22000000000000200000000002-20000000000000000000000000000
χ8344-4-44-2-2-4-4-444-400-44222-2-22-2400-4400000-22222-2000000000000-200000000002-20000000000000000000000000000
χ8444-4-44-2-2-4-4-44-44004-4222-2-22-24004-4000002-222-22000000000000-20000000000-220000000000000000000000000000
χ8588-88-8880000000000-800008-8000000000000000000000000000000000000000000000000000000000000000000000
χ8688-88-8-4-400000000004−4i34i34i3−4i3-44000000000000000000000000000000000000000000000000000000000000000000000
χ8788-88-8-4-4000000000044i3−4i3−4i34i3-44000000000000000000000000000000000000000000000000000000000000000000000
χ888-80008-84-40000000000000000000000000004-40000004-44-4000000000000000000000000000000000000000000000
χ898-80008-84-40000000000000000000000000004-4000000-44-44000000000000000000000000000000000000000000000
χ908-80008-8-44000000000000000000000000000-440000004-4-44000000000000000000000000000000000000000000000
χ918-80008-8-44000000000000000000000000000-44000000-444-4000000000000000000000000000000000000000000000
χ9216-16000-888-8000000000000000000000000000-440000000000000000000000000000000000000000000000000000000
χ9316-16000-88-880000000000000000000000000004-40000000000000000000000000000000000000000000000000000000

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