Finite Group Databasebeta

← Group #72271724

Character table — Group #72271724

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222222244444444444488888888888121216161616161616161616161616161616161616161616161616161616161624242424242424242432323232484848484848489696
order12222344446886668881212121224244488242424242424242224444466881212121216161616242424244848484848484848244444488121212122481616161648
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-11-1-1-1-111
χ311111111111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-111111-1-1
χ5111111111111111111111111111111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11111-1-1
χ7111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-111-1-1-1-1-111
χ91111111111111111111111111-1-1-1-1111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-11-111111111-1-1-1-1-111-1-11-1
χ101111111111111111111111111-1-1-1-1111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-1-1-1-111-1-11111-1-1-1111-1
χ111111111111111111111111111-1-1-1-1111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-11-111111111-1-1-1-1-1-1-111-11
χ121111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-11-1-1-1-1-111-1-11111-111-1-1-11
χ131111111111111111111111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-11-1-1-1-1-1-111-1-1111-1-111-11
χ141111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111-111111-1-1-1-111-1-1111-1-1-11
χ151111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-11-1-1-1-1-1-111-1-111111-1-11-1
χ161111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-11-111111-1-1-1-111-1-11-1-1111-1
χ1722222222222-2-2222-2-2-22222-2-222-2-2-2-2-2-2-2-2-2220000000000002200000000000000002220000-2-2000000-2000000
χ1822222222222-2-2222-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2-20000220000002000000
χ1922222222222-2-2222-2-2-22222-2-2-2-222-2-2-2222222000000000000-2-20000000000000000-22-20000-2-20000002000000
χ2022222222222-2-2222-2-2-22222-2-2-2-222-2-2-22222-2-2000000000000-2-200000000000000002-22000022000000-2000000
χ2122222-12222-122-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-100222222-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000-1-1-1-1000000000
χ2222222-12222-122-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-10022-2-2-2-2-1-122-1-1-1-1-2-2-2-2-1-1-1-1111111110000000001111000000000
χ2322222-12222-122-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-100-2-2222211-2-211-1-1-2-2-2-2111111111111000000000-1-1-1-1000000000
χ2422222-12222-122-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-100-2-2-2-2-2-211-2-211-1-122221111-1-1-1-1-1-1-1-10000000001111000000000
χ2522222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-1-1-11111002222-2-2-1-1-2-2-1-11122-2-21111-1-1-1-11111000000000-1-111000000000
χ2622222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-1-1-111110022-2-222-1-1-2-2-1-111-2-22211111111-1-1-1-100000000011-1-1000000000
χ2722222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-1-1-1111100-2-222-2-211221111-2-222-1-1-1-11111-1-1-1-1000000000-1-111000000000
χ2822222-12222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-1-1-1111100-2-2-2-2221122111122-2-2-1-1-1-1-1-1-1-1111100000000011-1-1000000000
χ29222-2-222-2-222222-2-2-22-22-22-22200002-2-2000000000000002i−2i000000002i2i−2i−2i000000000002i2i−2i−2i000000000002-200
χ30222-2-222-2-222222-2-2-22-22-22-22200002-2-2000000000000002i−2i000000002i2i−2i−2i00000000000−2i−2i2i2i00000000000-2200
χ31222-2-222-2-222222-2-2-22-22-22-22200002-2-200000000000000−2i2i00000000−2i−2i2i2i000000000002i2i−2i−2i00000000000-2200
χ32222-2-222-2-222222-2-2-22-22-22-22200002-2-200000000000000−2i2i00000000−2i−2i2i2i00000000000−2i−2i2i2i000000000002-200
χ3322-22-22-2-2222-2-2-22-222-2-222-2-2-2000022-20000002-200002200-2-20000000000000000000002i−2i2i−2i0000000002i−2i0000
χ3422-22-22-2-2222-2-2-22-222-2-222-2-2-2000022-20000002-200002200-2-2000000000000000000000−2i2i−2i2i000000000−2i2i0000
χ3522-22-22-2-2222-2-2-22-222-2-222-2-2-2000022-2000000-220000-2-200220000000000000000000002i−2i2i−2i000000000−2i2i0000
χ3622-22-22-2-2222-2-2-22-222-2-222-2-2-2000022-2000000-220000-2-20022000000000000000000000−2i2i−2i2i0000000002i−2i0000
χ3722-2-222-22-22222-2-222-2-2-2-222222-22-2-22-222-2-200002-22-20000002-200000000000000000000000002-22-2000000000
χ3822-2-222-22-22222-2-222-2-2-2-222222-22-2-22-222-2-20000-22-220000002-20000000000000000000000000-22-22000000000
χ3922-2-222-22-22222-2-222-2-2-2-22222-22-22-22-2-2-22200002-2-22000000-2200000000000000000000000002-2-22000000000
χ4022-2-222-22-22222-2-222-2-2-2-22222-22-22-22-2-2-2220000-222-2000000-220000000000000000000000000-222-2000000000
χ4122-2-222-22-222-2-2-2-22-222-2-222-2-22-2-222-22-2-222000000000000002-200000000000000000002-2-220000002-20000000
χ4222-2-222-22-222-2-2-2-22-222-2-222-2-22-2-222-22-2-222000000000000002-20000000000000000000-222-2000000-220000000
χ4322-2-222-22-222-2-2-2-22-222-2-222-2-2-222-22-2222-2-200000000000000-2200000000000000000002-2-22000000-220000000
χ4422-2-222-22-222-2-2-2-22-222-2-222-2-2-222-22-2222-2-200000000000000-220000000000000000000-222-20000002-20000000
χ4522-2-22-1-22-22-12211-12-2-211-1-1-1-12-22-21-11-1-11100002-22-2−i3i300−i3i3-110000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3000000000-11-11000000000
χ4622-2-22-1-22-22-12211-12-2-211-1-1-1-12-22-21-11-1-11100002-22-2i3−i300i3−i3-110000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3000000000-11-11000000000
χ4722-2-22-1-22-22-12211-12-2-211-1-1-1-12-22-21-11-1-1110000-22-22−i3i300−i3i3-110000−i3i3−i3i3i3i3−i3−i3i3i3−i3−i30000000001-11-1000000000
χ4822-2-22-1-22-22-12211-12-2-211-1-1-1-12-22-21-11-1-1110000-22-22i3−i300i3−i3-110000i3−i3i3−i3−i3−i3i3i3−i3−i3i3i30000000001-11-1000000000
χ4922-2-22-1-22-22-12211-12-2-211-1-1-1-1-22-221-1111-1-100002-2-22−i3i300−i3i31-10000i3−i3i3−i3−i3−i3i3i3i3i3−i3−i3000000000-111-1000000000
χ5022-2-22-1-22-22-12211-12-2-211-1-1-1-1-22-221-1111-1-100002-2-22i3−i300i3−i31-10000−i3i3−i3i3i3i3−i3−i3−i3−i3i3i3000000000-111-1000000000
χ5122-2-22-1-22-22-12211-12-2-211-1-1-1-1-22-221-1111-1-10000-222-2−i3i300−i3i31-10000i3−i3i3−i3i3i3−i3−i3−i3−i3i3i30000000001-1-11000000000
χ5222-2-22-1-22-22-12211-12-2-211-1-1-1-1-22-221-1111-1-10000-222-2i3−i300i3−i31-10000−i3i3−i3i3−i3−i3i3i3i3i3−i3−i30000000001-1-11000000000
χ53444444-4-4-4-4400444000-4-4-4-40000000000000440000000000000000000000000000000-400000000000000000000
χ54444444-4-4-4-4400444000-4-4-4-40000000000000-4-40000000000000000000000000000000400000000000000000000
χ5544444-24444-2-4-4-2-2-2-4-4-4-2-2-2-22244-4-4222222200000000000000-2-200000000000000000000000000000000000000
χ5644444-24444-2-4-4-2-2-2-4-4-4-2-2-2-222-4-444222-2-2-2-2000000000000002200000000000000000000000000000000000000
χ57444-4-444-4-444-4-44-4-44-444-44-4-4-40000-4440000000000000000000000000000000000000000000000000000000000
χ58444-4-44-444-44004-4-4000-44-440000000000000000000000000000000−2i22i200000000−2i22i2−2i22i20000000000000000000000
χ59444-4-44-444-44004-4-4000-44-4400000000000000000000000000000002i2−2i2000000002i2−2i22i2−2i20000000000000000000000
χ60444-4-4-24-4-44-244-222-44-4-22-22-2-20000-222000000000000004i−4i00000000−2i−2i2i2i000000000000000000000000000000
χ61444-4-4-24-4-44-244-222-44-4-22-22-2-20000-22200000000000000−4i4i000000002i2i−2i−2i000000000000000000000000000000
χ62444-4-4-24-4-44-2-4-4-2224-44-22-222200002-2-2000000000000−2i32i3002i3−2i30000000000000000000000000000000000000000
χ63444-4-4-24-4-44-2-4-4-2224-44-22-222200002-2-20000000000002i3−2i300−2i32i30000000000000000000000000000000000000000
χ64444-4-4-2-444-4-200-2220002-22-2000000000−2i32i3−2i32i3000000000000000000−2i22i200006−66−6i2−i2i2−i20000000000000000000000
χ65444-4-4-2-444-4-200-2220002-22-2000000000−2i32i3−2i32i30000000000000000002i2−2i20000−66−66−i2i2−i2i20000000000000000000000
χ66444-4-4-2-444-4-200-2220002-22-20000000002i3−2i32i3−2i3000000000000000000−2i22i20000−66−66i2−i2i2−i20000000000000000000000
χ67444-4-4-2-444-4-200-2220002-22-20000000002i3−2i32i3−2i30000000000000000002i2−2i200006−66−6−i2i2−i2i20000000000000000000000
χ6844-44-4444-4-4400-44-40004-4-4400000000000000000000000000000−2i22i2000000−2i22i22i2−2i200000000000000000000000000
χ6944-44-4444-4-4400-44-40004-4-44000000000000000000000000000002i2−2i20000002i2−2i2−2i22i200000000000000000000000000
χ7044-44-44-4-444444-44-4-4-44-444-4440000-4-440000000000000000000000000000000000000000000000000000000000
χ7144-44-4-244-4-4-2002-22000-222-2000000000−2i32i32i3−2i30000000000000000−2i22i2000000i2−i2−i2i26−6−660000000000000000000000
χ7244-44-4-244-4-4-2002-22000-222-2000000000−2i32i32i3−2i300000000000000002i2−2i2000000−i2i2i2−i2−666−60000000000000000000000
χ7344-44-4-244-4-4-2002-22000-222-20000000002i3−2i3−2i32i30000000000000000−2i22i2000000i2−i2−i2i2−666−60000000000000000000000
χ7444-44-4-244-4-4-2002-22000-222-20000000002i3−2i3−2i32i300000000000000002i2−2i2000000−i2i2i2−i26−6−660000000000000000000000
χ7544-44-4-2-4-444-2442-22-4-442-2-22-2-2000022-200000000000000000000000023−23−2323000000000000000000000000000000
χ7644-44-4-2-4-444-2442-22-4-442-2-22-2-2000022-2000000000000000000000000−232323−23000000000000000000000000000000
χ7744-44-4-2-4-444-2-4-42-2244-42-2-22220000-2-220000004-40000-2-200220000000000000000000000000000000000000000
χ7844-44-4-2-4-444-2-4-42-2244-42-2-22220000-2-22000000-4400002200-2-20000000000000000000000000000000000000000
χ7944-4-4444-44-4400-4-4400044-4-400000000000000000000000000000000000000000000040-40000000000000000000
χ8044-4-4444-44-4400-4-4400044-4-4000000000000000000000000000000000000000000000-4040000000000000000000
χ8144-4-44-2-44-44-2-4-422-2-44422-2-2224-4-44-22-222-2-200000000000000-2200000000000000000000000000000000000000
χ8244-4-44-2-44-44-2-4-422-2-44422-2-222-444-4-22-2-2-222000000000000002-200000000000000000000000000000000000000
χ8388888-4-8-8-8-8-400-4-4-400044440000000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-48-88-8-40044-4000-4-4440000000000000000000000000000000000000000000000000000000000000000000
χ858-800080000-8−4i24i20000000000−4i24i2000000000004-40000000000000000000000000000000000000−2i22i20000000000000
χ868-800080000-8−4i24i20000000000−4i24i200000000000-4400000000000000000000000000000000000002i2−2i20000000000000
χ878-800080000-84i2−4i200000000004i2−4i2000000000004-400000000000000000000000000000000000002i2−2i20000000000000
χ888-800080000-84i2−4i200000000004i2−4i200000000000-440000000000000000000000000000000000000−2i22i20000000000000
χ8916-16000-800008−8i28i200000000004i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ9016-16000-8000088i2−8i20000000000−4i24i200000000000000000000000000000000000000000000000000000000000000000

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