Finite Group Databasebeta

← Group #72271602

Character table — Group #72271602

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222222244444444444448888888888816161616161616161616161616161616161616161616161616161616161624242424242424243232323248484848484848489696
order12222344446666888812121212242444882424242424242424444466881212121216161616242424244848484848484848222244441212121244881616161648
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1
χ41111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ511111111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ9111111111111111111111111-1-1-1-1111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11-111-1-11-1
χ10111111111111111111111111-1-1-1-1111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-111-11
χ11111111111111111111111111-1-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1111-1-1-11
χ12111111111111111111111111-1-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1111-1
χ13111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-11-1-1-111-11
χ14111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1111-1-11-1
χ15111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-11111-1-111-1-111-1-1-11-1-1111-1
χ16111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1-11
χ1722222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-200000000000022000000000000000000002222000000-2-2000000
χ1822222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-20000000000002200000000000000000000-2-2-2-200000022000000
χ1922222222222222-2-2-2-22222-2-2-2-222-2-2-22222000000000000-2-20000000000000000000022-2-2000000-22000000
χ2022222222222222-2-2-2-22222-2-2-2-222-2-2-22222000000000000-2-200000000000000000000-2-2220000002-2000000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1222222-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-122-2-2-2-2-1-122-1-1-1-1-2-2-2-2-1-1-1-1111111110000000011110000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-2-2222211-2-211-1-1-2-2-2-211111111111100000000-1-1-1-10000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-2-2-2-2-2-211-2-211-1-122221111-1-1-1-1-1-1-1-10000000011110000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-111112222-2-2-1-1-2-2-1-11122-2-21111-1-1-1-1111100000000-1-1110000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1111122-2-222-1-1-2-2-1-111-2-22211111111-1-1-1-10000000011-1-10000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-11111-2-222-2-211221111-2-222-1-1-1-11111-1-1-1-100000000-1-1110000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-11111-2-2-2-2221122111122-2-2-1-1-1-1-1-1-1-111110000000011-1-10000000000
χ29222-2-2222-2-222-2-22-22-22-22-2-2-2000022-200002-200002200-2-200000000000000000022-2-20000000000002-20000
χ30222-2-2222-2-222-2-22-22-22-22-2-2-2000022-200002-200002200-2-2000000000000000000-2-222000000000000-220000
χ31222-2-2222-2-222-2-22-22-22-22-2-2-2000022-20000-220000-2-2002200000000000000000022-2-2000000000000-220000
χ32222-2-2222-2-222-2-22-22-22-22-2-2-2000022-20000-220000-2-20022000000000000000000-2-2220000000000002-20000
χ3322-22-22-222-22-22-2-222-2-222-22200002-2-20000000000002i−2i000000002i2i−2i−2i000000002-22-2000000000000002i−2i00
χ3422-22-22-222-22-22-2-222-2-222-22200002-2-20000000000002i−2i000000002i2i−2i−2i00000000-22-2200000000000000−2i2i00
χ3522-22-22-222-22-22-2-222-2-222-22200002-2-2000000000000−2i2i00000000−2i−2i2i2i000000002-22-200000000000000−2i2i00
χ3622-22-22-222-22-22-2-222-2-222-22200002-2-2000000000000−2i2i00000000−2i−2i2i2i00000000-22-22000000000000002i−2i00
χ3722-2-222-22-222-2-2222-2-2-2-222222-22-2-22-222-2-2002-22-20000002-20000000000000000000000002-22-20000000000
χ3822-2-222-22-222-2-2222-2-2-2-222222-22-2-22-222-2-200-22-220000002-2000000000000000000000000-22-220000000000
χ3922-2-222-22-222-2-2222-2-2-2-22222-22-22-22-2-2-222002-2-22000000-220000000000000000000000002-2-220000000000
χ4022-2-222-22-222-2-2222-2-2-2-22222-22-22-22-2-2-22200-222-2000000-22000000000000000000000000-222-20000000000
χ4122-2-222-22-222-2-22-2-222-2-222-2-22-2-222-22-2-2220000000000002-200000000000000002-2-22000000002-200000000
χ4222-2-222-22-222-2-22-2-222-2-222-2-22-2-222-22-2-2220000000000002-20000000000000000-222-200000000-2200000000
χ4322-2-222-22-222-2-22-2-222-2-222-2-2-222-22-2222-2-2000000000000-2200000000000000002-2-2200000000-2200000000
χ4422-2-222-22-222-2-22-2-222-2-222-2-2-222-22-2222-2-2000000000000-220000000000000000-222-2000000002-200000000
χ4522-2-22-1-22-22-111-122-2-211-1-1-1-12-22-21-11-1-111002-22-2−i3i300−i3i3-110000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300000000-11-110000000000
χ4622-2-22-1-22-22-111-122-2-211-1-1-1-12-22-21-11-1-111002-22-2i3−i300i3−i3-110000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300000000-11-110000000000
χ4722-2-22-1-22-22-111-122-2-211-1-1-1-12-22-21-11-1-11100-22-22−i3i300−i3i3-110000−i3i3−i3i3i3i3−i3−i3i3i3−i3−i3000000001-11-10000000000
χ4822-2-22-1-22-22-111-122-2-211-1-1-1-12-22-21-11-1-11100-22-22i3−i300i3−i3-110000i3−i3i3−i3−i3−i3i3i3−i3−i3i3i3000000001-11-10000000000
χ4922-2-22-1-22-22-111-122-2-211-1-1-1-1-22-221-1111-1-1002-2-22−i3i300−i3i31-10000i3−i3i3−i3−i3−i3i3i3i3i3−i3−i300000000-111-10000000000
χ5022-2-22-1-22-22-111-122-2-211-1-1-1-1-22-221-1111-1-1002-2-22i3−i300i3−i31-10000−i3i3−i3i3i3i3−i3−i3−i3−i3i3i300000000-111-10000000000
χ5122-2-22-1-22-22-111-122-2-211-1-1-1-1-22-221-1111-1-100-222-2−i3i300−i3i31-10000i3−i3i3−i3i3i3−i3−i3−i3−i3i3i3000000001-1-110000000000
χ5222-2-22-1-22-22-111-122-2-211-1-1-1-1-22-221-1111-1-100-222-2i3−i300i3−i31-10000−i3i3−i3i3−i3−i3i3i3i3i3−i3−i3000000001-1-110000000000
χ53444444-4-4-4-444440000-4-4-4-4000000000000000000000000000000000000000000000004-40000000000000000
χ54444444-4-4-4-444440000-4-4-4-400000000000000000000000000000000000000000000000-440000000000000000
χ5544444-24444-2-2-2-2-4-4-4-4-2-2-2-22244-4-42222222000000000000-2-200000000000000000000000000000000000000
χ5644444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-444222-2-2-2-20000000000002200000000000000000000000000000000000000
χ57444-4-4444-4-444-4-4-44-444-44-4440000-4-4400000000000000000000000000000000000000000000000000000000
χ58444-4-44-4-44444-4-40000-44-44000000000000000000000000000−2i22i2000000−2i22i2−2i22i200000000000000000000000000
χ59444-4-44-4-44444-4-40000-44-440000000000000000000000000002i2−2i20000002i2−2i22i2−2i200000000000000000000000000
χ60444-4-4-244-4-4-2-2224-44-4-22-22220000-2-2200004-40000-2-200220000000000000000000000000000000000000000
χ61444-4-4-244-4-4-2-2224-44-4-22-22220000-2-220000-4400002200-2-20000000000000000000000000000000000000000
χ62444-4-4-244-4-4-2-222-44-44-22-22-2-2000022-2000000000000000000000023−23−2323000000000000000000000000000000
χ63444-4-4-244-4-4-2-222-44-44-22-22-2-2000022-20000000000000000000000−232323−23000000000000000000000000000000
χ64444-4-4-2-4-444-2-22200002-22-2000000000−2i32i3−2i32i300000000000000−2i22i2000000i2−i2i2−i26−66−60000000000000000000000
χ65444-4-4-2-4-444-2-22200002-22-2000000000−2i32i3−2i32i3000000000000002i2−2i2000000−i2i2−i2i2−66−660000000000000000000000
χ66444-4-4-2-4-444-2-22200002-22-20000000002i3−2i32i3−2i300000000000000−2i22i2000000i2−i2i2−i2−66−660000000000000000000000
χ67444-4-4-2-4-444-2-22200002-22-20000000002i3−2i32i3−2i3000000000000002i2−2i2000000−i2i2−i2i26−66−60000000000000000000000
χ6844-44-444-4-444-44-400004-4-4400000000000000000000000000000−2i22i200000000−2i22i22i2−2i20000000000000000000000
χ6944-44-444-4-444-44-400004-4-44000000000000000000000000000002i2−2i2000000002i2−2i2−2i22i20000000000000000000000
χ7044-44-44-444-44-44-44-4-44-444-4-4-40000-44400000000000000000000000000000000000000000000000000000000
χ7144-44-4-24-4-44-22-220000-222-2000000000−2i32i32i3−2i30000000000000000−2i22i200006−6−66i2−i2−i2i20000000000000000000000
χ7244-44-4-24-4-44-22-220000-222-2000000000−2i32i32i3−2i300000000000000002i2−2i20000−666−6−i2i2i2−i20000000000000000000000
χ7344-44-4-24-4-44-22-220000-222-20000000002i3−2i3−2i32i30000000000000000−2i22i20000−666−6i2−i2−i2i20000000000000000000000
χ7444-44-4-24-4-44-22-220000-222-20000000002i3−2i3−2i32i300000000000000002i2−2i200006−6−66−i2i2i2−i20000000000000000000000
χ7544-44-4-2-444-4-22-224-4-442-2-222200002-2-20000000000−2i32i3002i3−2i30000000000000000000000000000000000000000
χ7644-44-4-2-444-4-22-224-4-442-2-222200002-2-200000000002i3−2i300−2i32i30000000000000000000000000000000000000000
χ7744-44-4-2-444-4-22-22-444-42-2-22-2-20000-2220000000000004i−4i00000000−2i−2i2i2i000000000000000000000000000000
χ7844-44-4-2-444-4-22-22-444-42-2-22-2-20000-222000000000000−4i4i000000002i2i−2i−2i000000000000000000000000000000
χ7944-4-4444-44-44-4-44000044-4-400000000000000000000000000000000000000000000000004-400000000000000
χ8044-4-4444-44-44-4-44000044-4-40000000000000000000000000000000000000000000000000-4400000000000000
χ8144-4-44-2-44-44-222-2-4-44422-2-2224-4-44-22-222-2-2000000000000-2200000000000000000000000000000000000000
χ8244-4-44-2-44-44-222-2-4-44422-2-222-444-4-22-2-2-2220000000000002-200000000000000000000000000000000000000
χ8388888-4-8-8-8-8-4-4-4-40000444400000000000000000000000000000000000000000000000000000000000000000
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).