Finite Group Databasebeta

← Group #72271720

Character table — Group #72271720

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222222244444444448888888888888888161616161616161616161616161616161616161616161616242424243232323232324848484848484848484848484848
order12222344446121266688881212124444448824242424242424242466888812121212121212122424242424242424444448121224242222441616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-11-11111-1-1-1-1
χ61111111111111111111111111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111
χ71111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-111111-1-1-1-1
χ911111111111111111111111-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1-111-1-1-1-1-1-111111-111-1-1-11-1-1-1111-1-111-1-1
χ1011111111111111111111111-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-111-1-11-1111-1-1-111-1-111
χ1111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-111-1-111111111-11-1-111-11-1-1-11-1-111-1-111
χ1211111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-111-1-11111-1-1-1-1-11-1-1111-1111-111-1-111-1-1
χ1311111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-11-1-111-1-1-1-111-1-111-1-1-1-11111-11-1-111-1-111-1-111-1-1-1-111
χ1411111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-11-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-1
χ1511111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111-1-111111111111-111-1-1-1-111-1-1-1-11111-1-1
χ1611111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-11-111-1-111-1-11111-1-1-1-111
χ172222222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-20000-2-20000222222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022000022-2-2-2-222220000000000000000000000000000
χ192222222222222222-2-2-2-2222-2-222-2-2222222-2-2-2-20000-220000-2-222-2-2-2-2220000000000000000000000000000
χ202222222222222222-2-2-2-2222-2-2-2-222222222-2-2-2-200002-20000-2-2-2-22222-2-20000000000000000000000000000
χ2122222-12222-1-1-1-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222-12222-1-1-1-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-2-21122-2-211-1-1-1-1-1-1-1-1-1-111110000-2-2111100000000000000
χ2322222-12222-1-1-1-1-1-12222-1-1-122-2-2-2-222-1-1-1-1-1-1-1-122-1-1-2-222-1-1-1-111111111-1-1-1-10000-2-2111100000000000000
χ2422222-12222-1-1-1-1-1-12222-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-2-211-2-2-2-211-1-1111111111111000022-1-1-1-100000000000000
χ2522222-12222-1-1-1-1-1-12222-1-1-1-2-222-2-2-2-21111-1-1-1-122-1-12-2-2-2-1-111-1-111-1-111111100002-2-1-11100000000000000
χ2622222-12222-1-1-1-1-1-12222-1-1-1-2-222-2-2-2-21111-1-1-1-1-2-2112-2221111-1-111-1-111-1-1-1-10000-2211-1-100000000000000
χ2722222-12222-1-1-1-1-1-12222-1-1-1-2-2-2-222-2-21111-1-1-1-122-1-1-22-2-2-1-11111-1-111-1-111110000-2211-1-100000000000000
χ2822222-12222-1-1-1-1-1-12222-1-1-1-2-2-2-222-2-21111-1-1-1-1-2-211-2222111111-1-111-1-1-1-1-1-100002-2-1-11100000000000000
χ2922222-12222-1-1-1-1-1-1-2-2-2-2-1-1-1222222-2-21111111100−i3i3-2-200−i3i3-1-1-1-1-1-11111−i3−i3i3i3000000−i3i3−i3i300000000000000
χ3022222-12222-1-1-1-1-1-1-2-2-2-2-1-1-1222222-2-21111111100i3−i3-2-200i3−i3-1-1-1-1-1-11111i3i3−i3−i3000000i3−i3i3−i300000000000000
χ3122222-12222-1-1-1-1-1-1-2-2-2-2-1-1-122-2-2-2-2-2-21111111100−i3i32200−i3i3-1-11111-1-1-1-1−i3−i3i3i3000000i3−i3i3−i300000000000000
χ3222222-12222-1-1-1-1-1-1-2-2-2-2-1-1-122-2-2-2-2-2-21111111100i3−i32200i3−i3-1-11111-1-1-1-1i3i3−i3−i3000000−i3i3−i3i300000000000000
χ3322222-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-2-222-2-222-1-1-1-1111100−i3i3-2200−i3i311-1-11111-1-1i3i3−i3−i3000000−i3i3i3−i300000000000000
χ3422222-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-2-222-2-222-1-1-1-1111100i3−i3-2200i3−i311-1-11111-1-1−i3−i3i3i3000000i3−i3−i3i300000000000000
χ3522222-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1111100−i3i32-200−i3i31111-1-1-1-111i3i3−i3−i3000000i3−i3−i3i300000000000000
χ3622222-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1111100i3−i32-200i3−i31111-1-1-1-111−i3−i3i3i3000000−i3i3i3−i300000000000000
χ37222-2-2222-2-22-2-22-2-2-22-2222-200000000000022-2-22-2220000-2-2000000000000002i2i−2i−2i0000000000002i−2i000000
χ38222-2-2222-2-22-2-22-2-2-22-2222-200000000000022-2-22-2220000-2-200000000000000−2i−2i2i2i000000000000−2i2i000000
χ39222-2-2222-2-22-2-22-2-2-22-2222-200000000000022-2-2-22-2-2000022000000000000002i2i−2i−2i000000000000−2i2i000000
χ40222-2-2222-2-22-2-22-2-2-22-2222-200000000000022-2-2-22-2-200002200000000000000−2i−2i2i2i0000000000002i−2i000000
χ4122-22-22-222-22-2-2-22-222-2-2-2220000000000002-22-20000002i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000002-20000
χ4222-22-22-222-22-2-2-22-222-2-2-2220000000000002-22-20000002i−2i0000000000002i−2i2i−2i−2i2i−2i2i00000000000000-220000
χ4322-22-22-222-22-2-2-22-222-2-2-2220000000000002-22-2000000−2i2i000000000000−2i2i−2i2i2i−2i2i−2i00000000000000-220000
χ4422-22-22-222-22-2-2-22-222-2-2-2220000000000002-22-2000000−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000002-20000
χ4522-2-222-22-22222-2-222-2-22-22-22-200002-222-2-2-222-200000000002-20000000000000000000000022-20-200000000
χ4622-2-222-22-22222-2-222-2-22-22-22-200002-222-2-2-222-200000000002-200000000000000000000000-2-220200000000
χ4722-2-222-22-22222-2-222-2-22-22-2-220000-22-2-222-222-20000000000-22000000000000000000000002-220-200000000
χ4822-2-222-22-22222-2-222-2-22-22-2-220000-22-2-222-222-20000000000-2200000000000000000000000-22-20200000000
χ4922-2-222-22-22222-2-22-222-2-22-22-20000-22-2-2222-2-2200000000002-20000000000002-2-220000002000-2000000000
χ5022-2-222-22-22222-2-22-222-2-22-22-20000-22-2-2222-2-2200000000002-2000000000000-222-2000000-20002000000000
χ5122-2-222-22-22222-2-22-222-2-22-2-2200002-222-2-22-2-220000000000-220000000000002-2-22000000-20002000000000
χ5222-2-222-22-22222-2-22-222-2-22-2-2200002-222-2-22-2-220000000000-22000000000000-222-20000002000-2000000000
χ53444444-4-4-4-44-4-44440000-4-4-4004-40000000000000000000000004-40000000000000000000000000000000000
χ54444444-4-4-4-44-4-44440000-4-4-400-44000000000000000000000000-440000000000000000000000000000000000
χ5544444-2-4-4-4-4-222-2-2-20000222004-4000023−2323−230000000000000000-22000023−230000000000000000000000000000
χ5644444-2-4-4-4-4-222-2-2-20000222004-40000−2323−23230000000000000000-220000−23230000000000000000000000000000
χ5744444-2-4-4-4-4-222-2-2-2000022200-44000023−2323−2300000000000000002-20000−23230000000000000000000000000000
χ5844444-2-4-4-4-4-222-2-2-2000022200-440000−2323−232300000000000000002-2000023−230000000000000000000000000000
χ59444-4-4444-4-44-4-44-4-44-44-444-4000000000000-4-444000000000000000000000000000000000000000000000000
χ60444-4-44-4-4444444-4-40000-4-4400000000000000000000000000000000000000000000000000000000000022−2200
χ61444-4-44-4-4444444-4-40000-4-44000000000000000000000000000000000000000000000000000000000000−222200
χ62444-4-4-244-4-4-222-2224-44-4-2-2200000000000022-2-200−2i32i300002i3−2i300000000000000000000000000000000000000
χ63444-4-4-244-4-4-222-2224-44-4-2-2200000000000022-2-2002i3−2i30000−2i32i300000000000000000000000000000000000000
χ64444-4-4-244-4-4-222-222-44-44-2-22000000000000-2-2224-4-2-200002200000000000000000000000000000000000000
χ65444-4-4-244-4-4-222-222-44-44-2-22000000000000-2-222-44220000-2-200000000000000000000000000000000000000
χ6644-44-444-4-44444-44-400004-4-40000000000000000000000000000000000000000000000000000000000000022−22
χ6744-44-444-4-44444-44-400004-4-400000000000000000000000000000000000000000000000000000000000000−2222
χ6844-44-44-444-44-4-4-44-4-4-444-444000000000000-44-44000000000000000000000000000000000000000000000000
χ6944-44-4-2-444-4-2222-2244-4-42-2-2000000000000-22-220000004i−4i000000000000−2i2i−2i2i000000000000000000000000
χ7044-44-4-2-444-4-2222-2244-4-42-2-2000000000000-22-22000000−4i4i0000000000002i−2i2i−2i000000000000000000000000
χ7144-44-4-2-444-4-2222-22-4-4442-2-20000000000002-22-20000000000000000000023−23−2323000000000000000000000000
χ7244-44-4-2-444-4-2222-22-4-4442-2-20000000000002-22-200000000000000000000−232323−23000000000000000000000000
χ7344-4-4444-44-44-4-4-4-4400004-4400004-40000000000000000000000004-400000000000000000000000000000000
χ7444-4-4444-44-44-4-4-4-4400004-440000-44000000000000000000000000-4400000000000000000000000000000000
χ7544-4-44-24-44-4-22222-20000-22-200004-40023−23−2323000000000000000000-2223−23000000000000000000000000000000
χ7644-4-44-24-44-4-22222-20000-22-200004-400−232323−23000000000000000000-22−2323000000000000000000000000000000
χ7744-4-44-24-44-4-22222-20000-22-20000-440023−23−23230000000000000000002-2−2323000000000000000000000000000000
χ7844-4-44-24-44-4-22222-20000-22-20000-4400−232323−230000000000000000002-223−23000000000000000000000000000000
χ7944-4-44-2-44-44-2-2-222-24-4-442-224-400004-4-2-2222-2-220000000000-22000000000000000000000000000000000000
χ8044-4-44-2-44-44-2-2-222-24-4-442-22-440000-4422-2-22-2-2200000000002-2000000000000000000000000000000000000
χ8144-4-44-2-44-44-2-2-222-2-444-42-224-40000-4422-2-2-222-20000000000-22000000000000000000000000000000000000
χ8244-4-44-2-44-44-2-2-222-2-444-42-22-4400004-4-2-222-222-200000000002-2000000000000000000000000000000000000
χ83888-8-8-4-8-888-4-4-4-444000044-40000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-48-8-88-4-4-44-440000-4440000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-80000883−8300000000000000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-800008−838300000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).