Finite Group Databasebeta

← Group #72271404

Character table — Group #72271404

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222222224444444444888888888888881616161616161616161616161616161616161616161616161616162424242424243232323232484848484848484848484896
order1222234444666668888121212124444441212121224242424222466668121212121616161624244848484848484848444488681224242244888161616164
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1111-11-1-11-11-1-11111-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11-11-1-1-11-111-1-1-1-1111
χ7111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111-11-1111-11-1-1-1-1-1-1111
χ8111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1-11-111-11-1111111-1-1-1
χ911111111111111111111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ1011111111111111111111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ1111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1111-11-1-1-11-11-111-1-111-1
χ1411111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-11-11-1-11-11-11-1-111-1-11
χ1511111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-11-111-11-11-1-1-111-1-11
χ1611111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-11-1111-11-1111-1-111-1
χ17222222222222222-2-2-2-222220000222222-2-2-2-200000000-200000000-2-2000000002222-2-2000000000-20000000
χ18222222222222222-2-2-2-222220000222222-2-2-2-200000000-200000000-2-200000000-2-2-2-22200000000020000000
χ19222222222222222-2-2-2-222220000-2-2-2-2-2-2-2-2-2-200000000200000000220000000022-2-2-2-200000000020000000
χ20222222222222222-2-2-2-222220000-2-2-2-2-2-2-2-2-2-2000000002000000002200000000-2-22222000000000-20000000
χ2122222-12222-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000-12-1-1-1000000000000
χ2222222-12222-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-1-1-1-12-1-1-1-1-2-2-2-2-1-1111111110000001-2111000000000000
χ2322222-12222-1-1-1-1-12222-1-1-1-12222-2-21111-1-1-1-1-2-2221111-2-1-1-1-122-2-211-1-1-1-11111000000-1-2-111000000000000
χ2422222-12222-1-1-1-1-12222-1-1-1-12222-2-21111-1-1-1-1-2-2-2-21111-2-1-1-1-1-2-222111111-1-1-1-1000000121-1-1000000000000
χ2522222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-222111121111-2-2-2-2-1-111111111000000-12-1-1-1000000000000
χ2622222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-21111211112222-1-1-1-1-1-1-1-1-1-10000001-2111000000000000
χ2722222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-1-1-1-1-21111-2-222111111-1-1-1-1000000-1-2-111000000000000
χ2822222-12222-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-1-1-1-1-2111122-2-211-1-1-1-11111000000121-1-1000000000000
χ29222-2-2222-2-2222-2-2-2-22222-2-22i2i−2i−2i0000002-22-2002-2000002i2i−2i−2i2i−2i00002i2i−2i−2i000000000020-200000000000000
χ30222-2-2222-2-2222-2-2-2-22222-2-22i2i−2i−2i0000002-22-200-22000002i2i−2i−2i−2i2i0000−2i−2i2i2i0000000000-20200000000000000
χ31222-2-2222-2-2222-2-2-2-22222-2-2−2i−2i2i2i0000002-22-2002-200000−2i−2i2i2i−2i2i0000−2i−2i2i2i000000000020-200000000000000
χ32222-2-2222-2-2222-2-2-2-22222-2-2−2i−2i2i2i0000002-22-200-2200000−2i−2i2i2i2i−2i00002i2i−2i−2i0000000000-20200000000000000
χ33222-2-2-122-2-2-1-1-111-2-222-1-1112i2i−2i−2i0033−3−3-11-11002-2−i3−i3i3i30−i−iii2i−2i003−3−i−iii−i3−i3i3i3000000-1013−3000000000000
χ34222-2-2-122-2-2-1-1-111-2-222-1-1112i2i−2i−2i0033−3−3-11-1100-22−i3−i3i3i30−i−iii−2i2i003−3ii−i−ii3i3−i3−i300000010-1−33000000000000
χ35222-2-2-122-2-2-1-1-111-2-222-1-1112i2i−2i−2i00−3−333-11-11002-2i3i3−i3−i30−i−iii2i−2i00−33−i−iiii3i3−i3−i3000000-101−33000000000000
χ36222-2-2-122-2-2-1-1-111-2-222-1-1112i2i−2i−2i00−3−333-11-1100-22i3i3−i3−i30−i−iii−2i2i00−33ii−i−i−i3−i3i3i300000010-13−3000000000000
χ37222-2-2-122-2-2-1-1-111-2-222-1-111−2i−2i2i2i0033−3−3-11-11002-2i3i3−i3−i30ii−i−i−2i2i003−3ii−i−ii3i3−i3−i3000000-1013−3000000000000
χ38222-2-2-122-2-2-1-1-111-2-222-1-111−2i−2i2i2i0033−3−3-11-1100-22i3i3−i3−i30ii−i−i2i−2i003−3−i−iii−i3−i3i3i300000010-1−33000000000000
χ39222-2-2-122-2-2-1-1-111-2-222-1-111−2i−2i2i2i00−3−333-11-11002-2−i3−i3i3i30ii−i−i−2i2i00−33ii−i−i−i3−i3i3i3000000-101−33000000000000
χ40222-2-2-122-2-2-1-1-111-2-222-1-111−2i−2i2i2i00−3−333-11-1100-22−i3−i3i3i30ii−i−i2i−2i00−33−i−iiii3i3−i3−i300000010-13−3000000000000
χ4122-22-22-222-2-2-222-22-22-2-22-222i−2i2i−2i00000022-2-20000000002i−2i2i−2i0000000000000000000000000000002i−2i2-2000
χ4222-22-22-222-2-2-222-22-22-2-22-222i−2i2i−2i00000022-2-20000000002i−2i2i−2i000000000000000000000000000000−2i2i-22000
χ4322-22-22-222-2-2-222-22-22-2-22-22−2i2i−2i2i00000022-2-2000000000−2i2i−2i2i0000000000000000000000000000002i−2i-22000
χ4422-22-22-222-2-2-222-22-22-2-22-22−2i2i−2i2i00000022-2-2000000000−2i2i−2i2i000000000000000000000000000000−2i2i2-2000
χ4522-2-222-22-22-2-22-222-2-22-222-20000000000-222-22-2002-22-200000000000000000002-2002-200000020-200000000
χ4622-2-222-22-22-2-22-222-2-22-222-20000000000-222-22-2002-22-20000000000000000000-2200-22000000-20200000000
χ4722-2-222-22-22-2-22-222-2-22-222-20000000000-222-2-2200-22-2200000000000000000002-2002-2000000-20200000000
χ4822-2-222-22-22-2-22-222-2-22-222-20000000000-222-2-2200-22-220000000000000000000-2200-2200000020-200000000
χ4922-2-222-22-22-2-22-22-222-2-222-22-2-220000002-2-220000000002-2-22000000000000002-200-220000020-2000000000
χ5022-2-222-22-22-2-22-22-222-2-222-22-2-220000002-2-220000000002-2-2200000000000000-22002-200000-202000000000
χ5122-2-222-22-22-2-22-22-222-2-222-2-222-20000002-2-22000000000-222-2000000000000002-200-2200000-202000000000
χ5222-2-222-22-22-2-22-22-222-2-222-2-222-20000002-2-22000000000-222-200000000000000-22002-20000020-2000000000
χ53444444-4-4-4-4444440000-4-4-4-400000000000000000000000000000000000000000004-40000000000000000000
χ54444444-4-4-4-4444440000-4-4-4-40000000000000000000000000000000000000000000-440000000000000000000
χ5544444-24444-2-2-2-2-2-4-4-4-4-2-2-2-2000044-2-2-2-2222200000000-400000000220000000000000000000000000000000
χ5644444-24444-2-2-2-2-2-4-4-4-4-2-2-2-20000-4-42222222200000000400000000-2-20000000000000000000000000000000
χ57444-4-4444-4-4444-4-444-4-444-4-40000000000-44-4400000000000000000000000000000000000000000000000000
χ58444-4-44-4-444444-4-40000-4-444000000000000000000000000000000000000000000000000000000000000022−220
χ59444-4-44-4-444444-4-40000-4-4440000000000000000000000000000000000000000000000000000000000000−22220
χ60444-4-4-244-4-4-2-2-22244-4-4-2-2220000002323−23−232-22-200000000000000000−23230000000000000000000000000000000
χ61444-4-4-244-4-4-2-2-22244-4-4-2-222000000−23−2323232-22-20000000000000000023−230000000000000000000000000000000
χ6244-44-444-4-44-4-444-400004-44-40000000000000000000000000000022−2200000022−2222−2200000000000000000000000
χ6344-44-444-4-44-4-444-400004-44-400000000000000000000000000000−2222000000−2222−222200000000000000000000000
χ6444-44-44-444-4-4-444-4-44-44-44-440000000000-4-44400000000000000000000000000000000000000000000000000
χ6544-44-4-24-4-4422-2-220000-22-2200000023−2323−23000000000000000000022−22006−66−6−22−2200000000000000000000000
χ6644-44-4-24-4-4422-2-220000-22-2200000023−2323−230000000000000000000−222200−66−662−22−200000000000000000000000
χ6744-44-4-24-4-4422-2-220000-22-22000000−2323−2323000000000000000000022−2200−66−66−22−2200000000000000000000000
χ6844-44-4-24-4-4422-2-220000-22-22000000−2323−23230000000000000000000−2222006−66−62−22−200000000000000000000000
χ6944-44-4-2-444-422-2-224-44-42-22-24i−4i4i−4i000000-2-222000000000−2i2i−2i2i0000000000000000000000000000000000000
χ7044-44-4-2-444-422-2-224-44-42-22-2−4i4i−4i4i000000-2-2220000000002i−2i2i−2i0000000000000000000000000000000000000
χ7144-44-4-2-444-422-2-22-44-442-22-2000000000022-2-20000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ7244-44-4-2-444-422-2-22-44-442-22-2000000000022-2-200002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ7344-4-4444-44-4-4-44-4400004-4-4400004-44-4-44000000000000000000000000000000000000000000000000000000
χ7444-4-4444-44-4-4-44-4400004-4-440000-44-444-4000000000000000000000000000000000000000000000000000000
χ7544-4-44-24-44-422-22-20000-222-200004-4-222-200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000
χ7644-4-44-24-44-422-22-20000-222-200004-4-222-200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000
χ7744-4-44-24-44-422-22-20000-222-20000-442-2-2200000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000
χ7844-4-44-24-44-422-22-20000-222-20000-442-2-2200000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000
χ7944-4-44-2-44-4422-22-24-4-442-2-2200000000002-2-224-400-22-22000000000000000000000000000000000000000000
χ8044-4-44-2-44-4422-22-24-4-442-2-2200000000002-2-22-44002-22-2000000000000000000000000000000000000000000
χ8144-4-44-2-44-4422-22-2-444-42-2-224-4-44000000-222-2000000000-222-20000000000000000000000000000000000000
χ8244-4-44-2-44-4422-22-2-444-42-2-22-444-4000000-222-20000000002-2-220000000000000000000000000000000000000
χ8388888-4-8-8-8-8-4-4-4-4-4000044440000000000000000000000000000000000000000000000000000000000000000
χ84888-8-8-4-8-888-4-4-444000044-4-40000000000000000000000000000000000000000000000000000000000000000
χ8516-1600016000000-1600000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-80000−8i38i3800000000000000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-800008i3−8i3800000000000000000000000000000000000000000000000000000000000000000000000000

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