Finite Group Databasebeta

← Group #72271514

Character table — Group #72271514

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222222444444444444488888888888881616161616161616161616161616161616161616161616161616162424242424243232323232484848484848484848484896
order1222234444666688881212121224244444441212121224242422446681212121212121616161624244848484848484848444488461212122224888161616168
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-11-1111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-11-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ51111111111111111111111111111-1-1-1-1-1-1111-11-11-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-111-1-11-1-11-11111-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1111-11-11-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-111-11-1-1-1-1111
χ71111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1111-1-1111-1-11-1-1-1-1-1111
χ81111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-11-1-111-111-111111-1-1-1
χ9111111111111111111111111-1-1-1-1111111111-11-11-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-11
χ10111111111111111111111111-1-1-1-1111111111-11-11-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1
χ11111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ12111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-111-1-1-111-1-111-1-111-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-111-1-11-1-111-1-111-1-11
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-11-111-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111-1-111-111-1-1-1-111-1-11
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-11-111-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1111-1-11111-1-111-1
χ1722222222222222-2-2-2-22222-2-20000222222-2-2-2000000-20000000000-2-2000000002222-2-2000000000-20000000
χ1822222222222222-2-2-2-22222-2-20000222222-2-2-2000000-20000000000-2-200000000-2-2-2-22200000000020000000
χ1922222222222222-2-2-2-22222-2-20000-2-2-2-2-2-2-2-2-200000020000000000220000000022-2-2-2-200000000020000000
χ2022222222222222-2-2-2-22222-2-20000-2-2-2-2-2-2-2-2-2000000200000000002200000000-2-22222000000000-20000000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-12222-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-12-22-2-1-12-1-1-1-1-1-1-2-2-2-2-1-111111111000000-21111000000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-12222-2-21111-1-1-1-22-2211-211-1-1-1-122-2-211-1-1-1-11111000000-2-1-111000000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-12222-2-21111-1-1-1-2-2-2-211-211-1-1-1-1-2-222111111-1-1-1-1000000211-1-1000000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-22-22112111111-2-2-2-2-1-1111111110000002-1-1-1-1000000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-21121111112222-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-12222-1-1-2-1-11111-2-222111111-1-1-1-1000000-2-1-111000000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-12-22-2-1-1-2-1-1111122-2-211-1-1-1-11111000000211-1-1000000000000
χ29222-2-2222-2-222-2-2-2-2222-22-2-2-22i2i−2i−2i0000002-22020-2000002i2i−2i−2i2i−2i00002i2i−2i−2i000000000002-200000000000000
χ30222-2-2222-2-222-2-2-2-2222-22-2-2-22i2i−2i−2i0000002-220-202000002i2i−2i−2i−2i2i0000−2i−2i2i2i00000000000-2200000000000000
χ31222-2-2222-2-222-2-2-2-2222-22-2-2-2−2i−2i2i2i0000002-22020-200000−2i−2i2i2i−2i2i0000−2i−2i2i2i000000000002-200000000000000
χ32222-2-2222-2-222-2-2-2-2222-22-2-2-2−2i−2i2i2i0000002-220-20200000−2i−2i2i2i2i−2i00002i2i−2i−2i00000000000-2200000000000000
χ33222-2-2-122-2-2-1-111-2-222-11-11112i2i−2i−2i0033−3−3-11-1020-2−i3i30−i3i3−i−iii2i−2i003−3−i−iii−i3−i3i3i30000000-113−3000000000000
χ34222-2-2-122-2-2-1-111-2-222-11-11112i2i−2i−2i0033−3−3-11-10-202−i3i30−i3i3−i−iii−2i2i003−3ii−i−ii3i3−i3−i300000001-1−33000000000000
χ35222-2-2-122-2-2-1-111-2-222-11-11112i2i−2i−2i00−3−333-11-1020-2i3−i30i3−i3−i−iii2i−2i00−33−i−iiii3i3−i3−i30000000-11−33000000000000
χ36222-2-2-122-2-2-1-111-2-222-11-11112i2i−2i−2i00−3−333-11-10-202i3−i30i3−i3−i−iii−2i2i00−33ii−i−i−i3−i3i3i300000001-13−3000000000000
χ37222-2-2-122-2-2-1-111-2-222-11-1111−2i−2i2i2i0033−3−3-11-1020-2i3−i30i3−i3ii−i−i−2i2i003−3ii−i−ii3i3−i3−i30000000-113−3000000000000
χ38222-2-2-122-2-2-1-111-2-222-11-1111−2i−2i2i2i0033−3−3-11-10-202i3−i30i3−i3ii−i−i2i−2i003−3−i−iii−i3−i3i3i300000001-1−33000000000000
χ39222-2-2-122-2-2-1-111-2-222-11-1111−2i−2i2i2i00−3−333-11-1020-2−i3i30−i3i3ii−i−i−2i2i00−33ii−i−i−i3−i3i3i30000000-11−33000000000000
χ40222-2-2-122-2-2-1-111-2-222-11-1111−2i−2i2i2i00−3−333-11-10-202−i3i30−i3i3ii−i−i2i−2i00−33−i−iiii3i3−i3−i300000001-13−3000000000000
χ4122-22-22-222-22-22-22-22-2-222-2-2-22i−2i2i−2i00000022-20000000002i−2i2i−2i0000000000000000000000000000002i−2i2-2000
χ4222-22-22-222-22-22-22-22-2-222-2-2-22i−2i2i−2i00000022-20000000002i−2i2i−2i000000000000000000000000000000−2i2i-22000
χ4322-22-22-222-22-22-22-22-2-222-2-2-2−2i2i−2i2i00000022-2000000000−2i2i−2i2i0000000000000000000000000000002i−2i-22000
χ4422-22-22-222-22-22-22-22-2-222-2-2-2−2i2i−2i2i00000022-2000000000−2i2i−2i2i000000000000000000000000000000−2i2i2-2000
χ4522-2-222-22-222-2-222-2-22-2-222-2-20000000000-22220-20220-2-20000000000000000002-2002-20000002-2000000000
χ4622-2-222-22-222-2-222-2-22-2-222-2-20000000000-22220-20220-2-2000000000000000000-2200-22000000-22000000000
χ4722-2-222-22-222-2-222-2-22-2-222-2-20000000000-222-2020-2-20220000000000000000002-2002-2000000-22000000000
χ4822-2-222-22-222-2-222-2-22-2-222-2-20000000000-222-2020-2-2022000000000000000000-2200-220000002-2000000000
χ4922-2-222-22-222-2-22-222-2-2-222222-2-220000002-2-20000000002-2-22000000000000002-200-2200000200-200000000
χ5022-2-222-22-222-2-22-222-2-2-222222-2-220000002-2-20000000002-2-2200000000000000-22002-200000-200200000000
χ5122-2-222-22-222-2-22-222-2-2-22222-222-20000002-2-2000000000-222-2000000000000002-200-2200000-200200000000
χ5222-2-222-22-222-2-22-222-2-2-22222-222-20000002-2-2000000000-222-200000000000000-22002-200000200-200000000
χ53444444-4-4-4-444440000-4-4-4-40000004-44-44-400000000000000000000000000000000000000000000000000000
χ54444444-4-4-4-444440000-4-4-4-4000000-44-44-4400000000000000000000000000000000000000000000000000000
χ5544444-24444-2-2-2-2-4-4-4-4-2-2-2-222000044-2-2-2-2222000000-40000000000220000000000000000000000000000000
χ5644444-24444-2-2-2-2-4-4-4-4-2-2-2-2220000-4-4222222200000040000000000-2-20000000000000000000000000000000
χ5744444-2-4-4-4-4-2-2-2-2000022220000004-4-22-220000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ5844444-2-4-4-4-4-2-2-2-2000022220000004-4-22-220000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ5944444-2-4-4-4-4-2-2-2-200002222000000-442-22-20000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ6044444-2-4-4-4-4-2-2-2-200002222000000-442-22-20000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ61444-4-4444-4-444-4-444-4-44-44-4440000000000-44-400000000000000000000000000000000000000000000000000
χ62444-4-44-4-44444-4-40000-44-4400000000000000000000000000000022−2200000022−22−222200000000000000000000000
χ63444-4-44-4-44444-4-40000-44-44000000000000000000000000000000−2222000000−222222−2200000000000000000000000
χ64444-4-4-244-4-4-2-22244-4-4-22-22-2-20000002323−23−232-2200000000000000000−23230000000000000000000000000000000
χ65444-4-4-244-4-4-2-22244-4-4-22-22-2-2000000−23−2323232-220000000000000000023−230000000000000000000000000000000
χ66444-4-4-2-4-444-2-22200002-22-20000000023−23−232300000000000000000022−22006−6−66−222−200000000000000000000000
χ67444-4-4-2-4-444-2-22200002-22-20000000023−23−2323000000000000000000−222200−666−62−2−2200000000000000000000000
χ68444-4-4-2-4-444-2-22200002-22-200000000−232323−2300000000000000000022−2200−666−6−222−200000000000000000000000
χ69444-4-4-2-4-444-2-22200002-22-200000000−232323−23000000000000000000−2222006−6−662−2−2200000000000000000000000
χ7044-44-444-4-444-44-400004-4-440000000000000000000000000000000000000000000000000000000000000022−220
χ7144-44-444-4-444-44-400004-4-4400000000000000000000000000000000000000000000000000000000000000−22220
χ7244-44-44-444-44-44-4-44-44-444-4440000000000-4-4400000000000000000000000000000000000000000000000000
χ7344-44-4-2-444-4-22-224-44-42-2-22224i−4i4i−4i000000-2-22000000000−2i2i−2i2i0000000000000000000000000000000000000
χ7444-44-4-2-444-4-22-224-44-42-2-2222−4i4i−4i4i000000-2-220000000002i−2i2i−2i0000000000000000000000000000000000000
χ7544-44-4-2-444-4-22-22-44-442-2-22-2-2000000000022-20000−2i32i302i3−2i300000000000000000000000000000000000000000
χ7644-44-4-2-444-4-22-22-44-442-2-22-2-2000000000022-200002i3−2i30−2i32i300000000000000000000000000000000000000000
χ7744-4-4444-44-44-4-44000044-4-4000000000000000000000000000000000000000000004-40000000000000000000
χ7844-4-4444-44-44-4-44000044-4-400000000000000000000000000000000000000000000-440000000000000000000
χ7944-4-44-2-44-44-222-24-4-4422-2-22200000000002-2-240-40-2-202200000000000000000000000000000000000000000
χ8044-4-44-2-44-44-222-24-4-4422-2-22200000000002-2-2-4040220-2-200000000000000000000000000000000000000000
χ8144-4-44-2-44-44-222-2-444-422-2-2-2-24-4-44000000-222000000000-222-20000000000000000000000000000000000000
χ8244-4-44-2-44-44-222-2-444-422-2-2-2-2-444-4000000-2220000000002-2-220000000000000000000000000000000000000
χ8388-88-8-48-8-88-44-440000-444-400000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-48-88-8-444-40000-4-44400000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-8000080000000000046−46000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-80000800000000000−4646000000000000000000000000000000000000000000000000000000000000000

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