Finite Group Databasebeta

← Group #72271484

Character table — Group #72271484

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222222444444444444488888888888881616161616161616161616161616161616161616161616161616162424242424243232323232484848484848484848484896
order12222344446666888812121212242444444412121212242424246688812121212121216161616242448484848484848484444888242424242222448161616164
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-11-11-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111
χ51111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1-1111-1-1111-111-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-111-1-1-11-1-1111
χ71111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111111-1-11-1-1-11-1-1-1-1111
χ81111111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1111-1-1-1111-11111-1-1-1
χ9111111111111111111111111-1-1-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-11-111-1-1-1-11
χ10111111111111111111111111-1-1-1-1111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1
χ11111111111111111111111111-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1
χ12111111111111111111111111-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-111-1111-11-1-1-111-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1111-1-1-11-1111-1-11
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111111-1-1-111-1-1-1-111-1-11
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-11-1-11111-1-111-1
χ1722222222222222-2-2-2-22222-2-20000222222-2-2-20000-2000000000000-2-2000000002222-2-200000000000-200000
χ1822222222222222-2-2-2-22222-2-20000222222-2-2-20000-2000000000000-2-200000000-2-2-2-22200000000000200000
χ1922222222222222-2-2-2-22222-2-20000-2-2-2-2-2-2-2-2-200002000000000000220000000022-2-2-2-200000000000200000
χ2022222222222222-2-2-2-22222-2-20000-2-2-2-2-2-2-2-2-2000020000000000002200000000-2-2222200000000000-200000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-122-1-12-2-2-1-1-1-1-1-1-2-2-2-2-1-111111111000000-21111000000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-12222-2-21111-1-1-1-2-211-22211-1-1-1-122-2-211-1-1-1-11111000000-211-1-1000000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-12222-2-21111-1-1-1-2-211-2-2-211-1-1-1-1-2-222111111-1-1-1-10000002-1-111000000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-211222111111-2-2-2-2-1-1111111110000002-1-1-1-1000000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2112-2-21111112222-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-122-1-1-222-1-11111-2-222111111-1-1-1-1000000-211-1-1000000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-122-1-1-2-2-2-1-1111122-2-211-1-1-1-111110000002-1-111000000000000
χ29222-2-2222-2-222-2-2-22-2222-2-2222i2i−2i−2i000000-2-220000000002i2i−2i−2i000000000000000000000000000020-202i−2i000
χ30222-2-2222-2-222-2-2-22-2222-2-2222i2i−2i−2i000000-2-220000000002i2i−2i−2i0000000000000000000000000000-2020−2i2i000
χ31222-2-2222-2-222-2-2-22-2222-2-222−2i−2i2i2i000000-2-22000000000−2i−2i2i2i000000000000000000000000000020-20−2i2i000
χ32222-2-2222-2-222-2-2-22-2222-2-222−2i−2i2i2i000000-2-22000000000−2i−2i2i2i0000000000000000000000000000-20202i−2i000
χ3322-22-22-222-22-22-222-2-2-222-2222i−2i2i−2i0000002-2-2000002i−2i002i−2i2i−2i2-2000022-2-200000000000002i−2i000000000000
χ3422-22-22-222-22-22-222-2-2-222-2222i−2i2i−2i0000002-2-200000−2i2i002i−2i2i−2i-220000-2-2220000000000000−2i2i000000000000
χ3522-22-22-222-22-22-222-2-2-222-222−2i2i−2i2i0000002-2-2000002i−2i00−2i2i−2i2i-220000-2-22200000000000002i−2i000000000000
χ3622-22-22-222-22-22-222-2-2-222-222−2i2i−2i2i0000002-2-200000−2i2i00−2i2i−2i2i2-2000022-2-20000000000000−2i2i000000000000
χ3722-22-2-1-222-2-11-1122-2-21-1-11-1-12i−2i2i−2i0033−3−3-11100−i3i302i−2i−i3i3−ii−ii2-2003−3-1-11133−3−30000000−i3i3−ii000000000000
χ3822-22-2-1-222-2-11-1122-2-21-1-11-1-12i−2i2i−2i0033−3−3-11100−i3i30−2i2i−i3i3−ii−ii-22003−311-1-1−3−3330000000i3−i3i−i000000000000
χ3922-22-2-1-222-2-11-1122-2-21-1-11-1-12i−2i2i−2i00−3−333-11100i3−i302i−2ii3−i3−ii−ii2-200−33-1-111−3−3330000000i3−i3−ii000000000000
χ4022-22-2-1-222-2-11-1122-2-21-1-11-1-12i−2i2i−2i00−3−333-11100i3−i30−2i2ii3−i3−ii−ii-2200−3311-1-133−3−30000000−i3i3i−i000000000000
χ4122-22-2-1-222-2-11-1122-2-21-1-11-1-1−2i2i−2i2i0033−3−3-11100i3−i302i−2ii3−i3i−ii−i-22003−311-1-1−3−3330000000−i3i3−ii000000000000
χ4222-22-2-1-222-2-11-1122-2-21-1-11-1-1−2i2i−2i2i0033−3−3-11100i3−i30−2i2ii3−i3i−ii−i2-2003−3-1-11133−3−30000000i3−i3i−i000000000000
χ4322-22-2-1-222-2-11-1122-2-21-1-11-1-1−2i2i−2i2i00−3−333-11100−i3i302i−2i−i3i3i−ii−i-2200−3311-1-133−3−30000000i3−i3−ii000000000000
χ4422-22-2-1-222-2-11-1122-2-21-1-11-1-1−2i2i−2i2i00−3−333-11100−i3i30−2i2i−i3i3i−ii−i2-200−33-1-111−3−3330000000−i3i3i−i000000000000
χ4522-2-222-22-222-2-222-2-22-22-22-2-200000000002-222-222000-2-20000000000000000002-2002-20000002-2000000000
χ4622-2-222-22-222-2-222-2-22-22-22-2-200000000002-222-222000-2-2000000000000000000-2200-22000000-22000000000
χ4722-2-222-22-222-2-222-2-22-22-22-2-200000000002-22-22-2-2000220000000000000000002-2002-2000000-22000000000
χ4822-2-222-22-222-2-222-2-22-22-22-2-200000000002-22-22-2-200022000000000000000000-2200-220000002-2000000000
χ4922-2-222-22-222-2-22-222-2-22-22222-2-22000000-22-20000000002-2-22000000000000002-200-22000002000-20000000
χ5022-2-222-22-222-2-22-222-2-22-22222-2-22000000-22-20000000002-2-2200000000000000-22002-200000-200020000000
χ5122-2-222-22-222-2-22-222-2-22-2222-222-2000000-22-2000000000-222-2000000000000002-200-2200000-200020000000
χ5222-2-222-22-222-2-22-222-2-22-2222-222-2000000-22-2000000000-222-200000000000000-22002-2000002000-20000000
χ53444444-4-4-4-444440000-4-4-4-40000004-44-44-400000000000000000000000000000000000000000000000000000
χ54444444-4-4-4-444440000-4-4-4-4000000-44-44-4400000000000000000000000000000000000000000000000000000
χ5544444-24444-2-2-2-2-4-4-4-4-2-2-2-222000044-2-2-2-22220000-4000000000000220000000000000000000000000000000
χ5644444-24444-2-2-2-2-4-4-4-4-2-2-2-2220000-4-4222222200004000000000000-2-20000000000000000000000000000000
χ5744444-2-4-4-4-4-2-2-2-2000022220000004-4-22-2200000000000000000000006−66−66−66−600000000000000000000000
χ5844444-2-4-4-4-4-2-2-2-2000022220000004-4-22-220000000000000000000000−66−66−66−6600000000000000000000000
χ5944444-2-4-4-4-4-2-2-2-200002222000000-442-22-200000000000000000000006−66−6−66−6600000000000000000000000
χ6044444-2-4-4-4-4-2-2-2-200002222000000-442-22-20000000000000000000000−66−666−66−600000000000000000000000
χ61444-4-4444-4-444-4-44-44-444-4-4-4-4000000000044-400000000000000000000000000000000000000000000000000
χ62444-4-44-4-44444-4-40000-4-4440000000000000000000000000000000000000000000000000000000000000022−220
χ63444-4-44-4-44444-4-40000-4-44400000000000000000000000000000000000000000000000000000000000000−22220
χ64444-4-4-244-4-4-2-2224-44-4-2-222220000000000-2-2200−2i32i30002i3−2i300000000000000000000000000000000000000000
χ65444-4-4-244-4-4-2-2224-44-4-2-222220000000000-2-22002i3−2i3000−2i32i300000000000000000000000000000000000000000
χ66444-4-4-244-4-4-2-222-44-44-2-222-2-24i4i−4i−4i00000022-2000000000−2i−2i2i2i0000000000000000000000000000000000000
χ67444-4-4-244-4-4-2-222-44-44-2-222-2-2−4i−4i4i4i00000022-20000000002i2i−2i−2i0000000000000000000000000000000000000
χ6844-44-444-4-444-44-400004-4-4400000000000000000000000000000022−2200000022−22−222200000000000000000000000
χ6944-44-444-4-444-44-400004-4-44000000000000000000000000000000−2222000000−222222−2200000000000000000000000
χ7044-44-44-444-44-44-4-4-444-444-4-4-40000000000-44400000000000000000000000000000000000000000000000000
χ7144-44-4-24-4-44-22-220000-222-20000000023−23−232300000000000000000022−2200−666−6−222−200000000000000000000000
χ7244-44-4-24-4-44-22-220000-222-20000000023−23−2323000000000000000000−2222006−6−662−2−2200000000000000000000000
χ7344-44-4-24-4-44-22-220000-222-200000000−232323−2300000000000000000022−22006−6−66−222−200000000000000000000000
χ7444-44-4-24-4-44-22-220000-222-200000000−232323−23000000000000000000−222200−666−62−2−2200000000000000000000000
χ7544-44-4-2-444-4-22-22-4-4442-2-22220000002323−23−232-2-200000000000000000−23230000000000000000000000000000000
χ7644-44-4-2-444-4-22-22-4-4442-2-2222000000−23−2323232-2-20000000000000000023−230000000000000000000000000000000
χ7744-4-4444-44-44-4-4400004-44-4000000000000000000000000000000000000000000004-40000000000000000000
χ7844-4-4444-44-44-4-4400004-44-400000000000000000000000000000000000000000000-440000000000000000000
χ7944-4-44-2-44-44-222-24-4-442-22-2220000000000-22-24-4-2-20002200000000000000000000000000000000000000000
χ8044-4-44-2-44-44-222-24-4-442-22-2220000000000-22-2-4422000-2-200000000000000000000000000000000000000000
χ8144-4-44-2-44-44-222-2-444-42-22-2-2-24-4-440000002-22000000000-222-20000000000000000000000000000000000000
χ8244-4-44-2-44-44-222-2-444-42-22-2-2-2-444-40000002-220000000002-2-220000000000000000000000000000000000000
χ83888-8-8-4-8-888-4-444000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-48-88-8-444-40000-44-4400000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-8000080000000000046−46000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-80000800000000000−4646000000000000000000000000000000000000000000000000000000000000000

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