Finite Group Databasebeta

← Group #72271517

Character table — Group #72271517

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222222222444444444444888888888888812121616161616161616161616161616161616161616161616161616162424242424242432323232324848484848484848484896
order12222344446886668881212121224242444446612122424242244888121212121212121216161616242448484848484848484448888412122424224444161616168
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-11-11-111-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1111111111111111111111111111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111111
χ5111111111111111111111111111-1-1-1-1111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-11-11-1-1-1-1-1-11
χ6111111111111111111111111111-1-1-1-1111111111-1-11-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1
χ7111111111111111111111111111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1111111-1
χ8111111111111111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ91111111111111111111111111-1-11111-1-1-1-111111-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111111-1-111-1-1-1-1-111-1-1-1-11111-1-11
χ101111111111111111111111111-1-11111-1-1-1-111111-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1111-1-1-11-1111-1-111-1
χ111111111111111111111111111-1-11111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-111-1-1-1111111-1-1-1-111-1
χ121111111111111111111111111-1-11111-1-1-1-1111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-111111-1-11-11-1-1-111-1-11
χ131111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1-1111-11-1-1-1-1-1111
χ141111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1-111-1-1111-1-11111-1-111-1-1-1
χ151111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-111-1-1-111-11-111111-1-1-1
χ161111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-111-1-111111-1-1-1-1-1-111-1-1111
χ1722222222222-2-2222-2-2-22222-2-22200002222-2-2-22200-200000000000000-2-200000000222-2-2-2-20000000000000000
χ1822222222222-2-2222-2-2-22222-2-22200002222-2-2-2-2-200-200000000000000-2-200000000-2-2-222220000000000000000
χ1922222222222-2-2222-2-2-22222-2-2-2-20000-2-2-2-2-2-2-2220020000000000000022000000002-2-2-2-2220000000000000000
χ2022222222222-2-2222-2-2-22222-2-2-2-20000-2-2-2-2-2-2-2-2-2002000000000000002200000000-22222-2-20000000000000000
χ2122222-12222-122-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-10022222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000002-1-1-1-100000000000
χ2222222-12222-122-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-100222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000-2111100000000000
χ2322222-12222-122-1-1-1222-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-100-2-222211111111-2-2-2-2-1-11111111100000002-1-1-1-100000000000
χ2422222-12222-122-1-1-1222-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-100-2-22-2-2111111112222-1-1-1-1-1-1-1-1-1-10000000-2111100000000000
χ2522222-12222-122-1-1-1222-1-1-1-1-1-1-2-222221111-1-1-100-2-2-222-1-1-1-11111-2-222111111-1-1-1-10000000-211-1-100000000000
χ2622222-12222-122-1-1-1222-1-1-1-1-1-1-2-222221111-1-1-100-2-2-2-2-2-1-1-1-1111122-2-211-1-1-1-1111100000002-1-11100000000000
χ2722222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-10022-2221111-1-1-1-122-2-211-1-1-1-111110000000-211-1-100000000000
χ2822222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-10022-2-2-21111-1-1-1-1-2-222111111-1-1-1-100000002-1-11100000000000
χ29222-2-2222-2-22222-2-2-22-22-22-222002i2i−2i−2i0000-2-22000002i−2i2i2i−2i−2i0000002-200000022-2-200000000002i−2i00000000000
χ30222-2-2222-2-22222-2-2-22-22-22-222002i2i−2i−2i0000-2-2200000−2i2i2i2i−2i−2i000000-22000000-2-2220000000000−2i2i00000000000
χ31222-2-2222-2-22222-2-2-22-22-22-22200−2i−2i2i2i0000-2-22000002i−2i−2i−2i2i2i000000-22000000-2-22200000000002i−2i00000000000
χ32222-2-2222-2-22222-2-2-22-22-22-22200−2i−2i2i2i0000-2-2200000−2i2i−2i−2i2i2i0000002-200000022-2-20000000000−2i2i00000000000
χ33222-2-2-122-2-2-122-111-22-2-11-11-1-1002i2i−2i−2i−i3i3−i3i311-1000002i−2i−i−iii33−3−3002-2−i3i3−i3−i3i3i3-1-111000000003−3−ii00000000000
χ34222-2-2-122-2-2-122-111-22-2-11-11-1-1002i2i−2i−2i−i3i3−i3i311-100000−2i2i−i−iii33−3−300-22−i3i3i3i3−i3−i311-1-100000000−33i−i00000000000
χ35222-2-2-122-2-2-122-111-22-2-11-11-1-1002i2i−2i−2ii3−i3i3−i311-1000002i−2i−i−iii−3−333002-2i3−i3i3i3−i3−i3-1-11100000000−33−ii00000000000
χ36222-2-2-122-2-2-122-111-22-2-11-11-1-1002i2i−2i−2ii3−i3i3−i311-100000−2i2i−i−iii−3−33300-22i3−i3−i3−i3i3i311-1-1000000003−3i−i00000000000
χ37222-2-2-122-2-2-122-111-22-2-11-11-1-100−2i−2i2i2i−i3i3−i3i311-1000002i−2iii−i−i−3−33300-22−i3i3i3i3−i3−i311-1-1000000003−3−ii00000000000
χ38222-2-2-122-2-2-122-111-22-2-11-11-1-100−2i−2i2i2i−i3i3−i3i311-100000−2i2iii−i−i−3−333002-2−i3i3−i3−i3i3i3-1-11100000000−33i−i00000000000
χ39222-2-2-122-2-2-122-111-22-2-11-11-1-100−2i−2i2i2ii3−i3i3−i311-1000002i−2iii−i−i33−3−300-22i3−i3−i3−i3i3i311-1-100000000−33−ii00000000000
χ40222-2-2-122-2-2-122-111-22-2-11-11-1-100−2i−2i2i2ii3−i3i3−i311-100000−2i2iii−i−i33−3−3002-2i3−i3i3i3−i3−i3-1-111000000003−3i−i00000000000
χ4122-22-22-22-222-2-2-22-222-2-222-2-2-2002i−2i2i−2i00002-2200000002i−2i2i−2i000000000000000000000000000000020-200002i−2i0
χ4222-22-22-22-222-2-2-22-222-2-222-2-2-2002i−2i2i−2i00002-2200000002i−2i2i−2i0000000000000000000000000000000-2020000−2i2i0
χ4322-22-22-22-222-2-2-22-222-2-222-2-2-200−2i2i−2i2i00002-220000000−2i2i−2i2i000000000000000000000000000000020-20000−2i2i0
χ4422-22-22-22-222-2-2-22-222-2-222-2-2-200−2i2i−2i2i00002-220000000−2i2i−2i2i0000000000000000000000000000000-20200002i−2i0
χ4522-2-222-222-2222-2-222-2-2-2-2222200000000002-2-2002-200000002-22-20000000000000002-2002-20000000002-200000
χ4622-2-222-222-2222-2-222-2-2-2-2222200000000002-2-2002-200000002-22-2000000000000000-2200-22000000000-2200000
χ4722-2-222-222-2222-2-222-2-2-2-2222200000000002-2-200-220000000-22-220000000000000002-2002-2000000000-2200000
χ4822-2-222-222-2222-2-222-2-2-2-2222200000000002-2-200-220000000-22-22000000000000000-2200-220000000002-200000
χ4922-2-222-222-22-2-2-2-22-222-2-222-2-2002-2-220000-22200000002-2-2200000000000000000002-200-220000020-200000000
χ5022-2-222-222-22-2-2-2-22-222-2-222-2-2002-2-220000-22200000002-2-220000000000000000000-22002-200000-20200000000
χ5122-2-222-222-22-2-2-2-22-222-2-222-2-200-222-20000-2220000000-222-200000000000000000002-200-2200000-20200000000
χ5222-2-222-222-22-2-2-2-22-222-2-222-2-200-222-20000-2220000000-222-20000000000000000000-22002-20000020-200000000
χ53444444-4-4-4-4400444000-4-4-4-400000000000000044000000000000000000000000000-40000000000000000000000
χ54444444-4-4-4-4400444000-4-4-4-4000000000000000-4-400000000000000000000000000040000000000000000000000
χ5544444-24444-2-4-4-2-2-2-4-4-4-2-2-2-222440000-2-2-2-22220000-400000000000000220000000000000000000000000000000
χ5644444-24444-2-4-4-2-2-2-4-4-4-2-2-2-222-4-4000022222220000400000000000000-2-20000000000000000000000000000000
χ57444-4-4444-4-44-4-44-4-44-444-44-4-4-4000000000044-40000000000000000000000000000000000000000000000000000
χ58444-4-44-4-4444004-4-4000-44-4400000000000000000000000000000000000000000000000000000000000000−2i22i2000
χ59444-4-44-4-4444004-4-4000-44-44000000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ60444-4-4-244-4-4-2-4-4-2224-44-22-2222000000−2i32i3−2i32i3-2-2200000000000000000002i3−2i30000000000000000000000000000000
χ61444-4-4-244-4-4-2-4-4-2224-44-22-22220000002i3−2i32i3−2i3-2-220000000000000000000−2i32i30000000000000000000000000000000
χ6244-44-444-44-4400-44-40004-4-44000000000000000000000000000000−2i22i20000−2i22i2−2i22i2000000000000000000000000000
χ6344-44-444-44-4400-44-40004-4-440000000000000000000000000000002i2−2i200002i2−2i22i2−2i2000000000000000000000000000
χ6444-44-44-44-44444-44-4-4-44-444-4440000000000-44-40000000000000000000000000000000000000000000000000000
χ6544-44-4-24-44-4-2002-22000-222-200000000−2i32i32i3−2i3000000000000000000−2i22i20000i2−i2i2−i26−66−600000000000000000000000
χ6644-44-4-24-44-4-2002-22000-222-200000000−2i32i32i3−2i30000000000000000002i2−2i20000−i2i2−i2i2−66−6600000000000000000000000
χ6744-44-4-24-44-4-2002-22000-222-2000000002i3−2i3−2i32i3000000000000000000−2i22i20000i2−i2i2−i2−66−6600000000000000000000000
χ6844-44-4-24-44-4-2002-22000-222-2000000002i3−2i3−2i32i30000000000000000002i2−2i20000−i2i2−i2i26−66−600000000000000000000000
χ6944-44-4-2-44-44-2442-22-4-442-2-22-2-200000000002-220000000000023−23−23230000000000000000000000000000000000000
χ7044-44-4-2-44-44-2442-22-4-442-2-22-2-200000000002-2200000000000−232323−230000000000000000000000000000000000000
χ7144-44-4-2-44-44-2-4-42-2244-42-2-2222004i−4i4i−4i0000-22-20000000−2i2i−2i2i00000000000000000000000000000000000000000
χ7244-44-4-2-44-44-2-4-42-2244-42-2-222200−4i4i−4i4i0000-22-200000002i−2i2i−2i00000000000000000000000000000000000000000
χ7344-4-4444-4-44400-4-4400044-4-4004-4000044-4-40000000000000000000000000000000000000000000000000000000
χ7444-4-4444-4-44400-4-4400044-4-400-440000-4-4440000000000000000000000000000000000000000000000000000000
χ7544-4-44-24-4-44-20022-2000-2-222004-40000-2-2220000000000000000000000006−6−66−666−600000000000000000000000
χ7644-4-44-24-4-44-20022-2000-2-222004-40000-2-222000000000000000000000000−666−66−6−6600000000000000000000000
χ7744-4-44-24-4-44-20022-2000-2-22200-44000022-2-20000000000000000000000006−6−666−6−6600000000000000000000000
χ7844-4-44-24-4-44-20022-2000-2-22200-44000022-2-2000000000000000000000000−666−6−666−600000000000000000000000
χ7944-4-44-2-444-4-24422-24-4-422-2-2-2-20000000000-222004-40000000-22-220000000000000000000000000000000000000
χ8044-4-44-2-444-4-24422-24-4-422-2-2-2-20000000000-22200-4400000002-22-20000000000000000000000000000000000000
χ8144-4-44-2-444-4-2-4-422-2-44422-2-222004-4-4400002-2-20000000-222-200000000000000000000000000000000000000000
χ8244-4-44-2-444-4-2-4-422-2-44422-2-22200-444-400002-2-200000002-2-2200000000000000000000000000000000000000000
χ8388888-4-8-8-8-8-400-4-4-400044440000000000000000000000000000000000000000000000000000000000000000000
χ84888-8-8-4-8-888-400-4440004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ858-800080000-8−4i24i20000000000−4i24i200000000000004-4000000000000000000000000000000−2i22i2000000000000000000
χ868-800080000-8−4i24i20000000000−4i24i20000000000000-440000000000000000000000000000002i2−2i2000000000000000000
χ878-800080000-84i2−4i200000000004i2−4i200000000000004-40000000000000000000000000000002i2−2i2000000000000000000
χ888-800080000-84i2−4i200000000004i2−4i20000000000000-44000000000000000000000000000000−2i22i2000000000000000000
χ8916-16000-800008−8i28i200000000004i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ9016-16000-8000088i2−8i20000000000−4i24i200000000000000000000000000000000000000000000000000000000000000000

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