Finite Group Databasebeta

← Group #72271409

Character table — Group #72271409

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222222444444444444488888881212121212121212161616161616161616161616161616161616161616161616242424243232323232323232484848484848484848484848
order122223444466668888121212122424248824242444448888222444688121616161624244848484848484848448866612121224242444448816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ10111111111111111111111111-1-1-1-11111111111111-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111
χ11111111111111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ12111111111111111111111111-1-1-1-111111111111-1-1-1-111-111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ13111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ14111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1
χ15111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-111-1-1
χ16111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ1722222222222222-2-2-2-22222-2-222-2-2-2-2-22222-2-2-2-200000020020000-2-20000000022-2-200000000000000000000
χ1822222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2222200000020020000-2-200000000-2-22200000000000000000000
χ1922222222222222-2-2-2-22222-2-2-2-222-2-2-22222-2-2-2-2000000-200-200002200000000-2-22200000000000000000000
χ2022222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-22222000000-200-20000220000000022-2-200000000000000000000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-100000000222222-122-12222-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-10000000022-2-222-1-2-2-1-2-2-2-2-1-1111111110000-1-111-1-111000000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-100000000-2-222-2-2-122-1-2-2-2-2-1-111111111000011-1-111-1-1000000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-100000000-2-2-2-2-2-2-1-2-2-12222-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1000000002222-2-21-2-2122-2-211-1-1-1-111110000-1-1-1-11111000000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-10000000022-2-2-2-21221-2-222111111-1-1-1-10000-1-11111-1-1000000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-100000000-2-222221-2-21-2-222111111-1-1-1-1000011-1-1-1-111000000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-100000000-2-2-2-222122122-2-211-1-1-1-1111100001111-1-1-1-1000000000000
χ29222-2-22-222-222-2-22-22-2-2-2222200002-2-22i2i−2i−2i2i2i−2i−2i002-2000000000000000000000000002-200000000002i−2i0000
χ30222-2-22-222-222-2-22-22-2-2-2222200002-2-22i2i−2i−2i2i2i−2i−2i00-2200000000000000000000000000-220000000000−2i2i0000
χ31222-2-22-222-222-2-22-22-2-2-2222200002-2-2−2i−2i2i2i−2i−2i2i2i002-2000000000000000000000000002-20000000000−2i2i0000
χ32222-2-22-222-222-2-22-22-2-2-2222200002-2-2−2i−2i2i2i−2i−2i2i2i00-2200000000000000000000000000-2200000000002i−2i0000
χ33222-2-22-222-222-2-2-22-22-2-222-2-20000-2222i2i−2i−2i−2i−2i2i2i00000002-200000000000000000000000002-2002i−2i00000000
χ34222-2-22-222-222-2-2-22-22-2-222-2-20000-2222i2i−2i−2i−2i−2i2i2i0000000-220000000000000000000000000-2200−2i2i00000000
χ35222-2-22-222-222-2-2-22-22-2-222-2-20000-222−2i−2i2i2i2i2i−2i−2i00000002-200000000000000000000000002-200−2i2i00000000
χ36222-2-22-222-222-2-2-22-22-2-222-2-20000-222−2i−2i2i2i2i2i−2i−2i0000000-220000000000000000000000000-22002i−2i00000000
χ3722-22-2222-2-22-22-222-2-22-22-2220000-2-222i−2i2i−2i2i−2i2i−2i00000000002-2000022-2-20000000000000000000000002i−2i00
χ3822-22-2222-2-22-22-222-2-22-22-2220000-2-222i−2i2i−2i2i−2i2i−2i0000000000-220000-2-222000000000000000000000000−2i2i00
χ3922-22-2222-2-22-22-222-2-22-22-2220000-2-22−2i2i−2i2i−2i2i−2i2i00000000002-2000022-2-2000000000000000000000000−2i2i00
χ4022-22-2222-2-22-22-222-2-22-22-2220000-2-22−2i2i−2i2i−2i2i−2i2i0000000000-220000-2-2220000000000000000000000002i−2i00
χ4122-22-2222-2-22-22-2-2-2222-22-2-2-2000022-22i−2i2i−2i−2i2i−2i2i0000000000002i−2i0000002i2i−2i−2i00000000000000000000002-2
χ4222-22-2222-2-22-22-2-2-2222-22-2-2-2000022-22i−2i2i−2i−2i2i−2i2i000000000000−2i2i000000−2i−2i2i2i0000000000000000000000-22
χ4322-22-2222-2-22-22-2-2-2222-22-2-2-2000022-2−2i2i−2i2i2i−2i2i−2i0000000000002i−2i0000002i2i−2i−2i0000000000000000000000-22
χ4422-22-2222-2-22-22-2-2-2222-22-2-2-2000022-2−2i2i−2i2i2i−2i2i−2i000000000000−2i2i000000−2i−2i2i2i00000000000000000000002-2
χ4522-2-222-22-222-2-222-2-22-222-2220000-22-22-2-222-2-222-2000000000000000000000000002-200000000002-2000000
χ4622-2-222-22-222-2-222-2-22-222-2220000-22-22-2-222-2-22-2200000000000000000000000000-220000000000-22000000
χ4722-2-222-22-222-2-222-2-22-222-2220000-22-2-222-2-222-22-2000000000000000000000000002-20000000000-22000000
χ4822-2-222-22-222-2-222-2-22-222-2220000-22-2-222-2-222-2-2200000000000000000000000000-2200000000002-2000000
χ4922-2-222-22-222-2-22-222-2-222-2-2-200002-222-2-22-222-200002-2000000000000000000000000002-2002-20000000000
χ5022-2-222-22-222-2-22-222-2-222-2-2-200002-222-2-22-222-20000-2200000000000000000000000000-2200-220000000000
χ5122-2-222-22-222-2-22-222-2-222-2-2-200002-22-222-22-2-2200002-2000000000000000000000000002-200-220000000000
χ5222-2-222-22-222-2-22-222-2-222-2-2-200002-22-222-22-2-220000-2200000000000000000000000000-22002-20000000000
χ53444444-4-4-4-444440000-4-4-4-4000000000000000000000000000000000000000004-40000000000000000000000
χ54444444-4-4-4-444440000-4-4-4-400000000000000000000000000000000000000000-440000000000000000000000
χ5544444-24444-2-2-2-2-4-4-4-4-2-2-2-22244-4-422200000000000000-200-200002200000000000000000000000000000000
χ5644444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-4442220000000000000020020000-2-200000000000000000000000000000000
χ57444-4-444-4-4444-4-4000044-4-400004i−4i00000000000000000000000004i−4i00000000000000000000000000000000
χ58444-4-444-4-4444-4-4000044-4-40000−4i4i0000000000000000000000000−4i4i00000000000000000000000000000000
χ59444-4-4-24-4-44-2-2220000-2-22200004i−4i0000000000000000000000000−2i2ii6−i6i6−i66−66−6000000000000000000000000
χ60444-4-4-24-4-44-2-2220000-2-22200004i−4i0000000000000000000000000−2i2i−i6i6−i6i6−66−66000000000000000000000000
χ61444-4-4-24-4-44-2-2220000-2-2220000−4i4i00000000000000000000000002i−2ii6−i6i6−i6−66−66000000000000000000000000
χ62444-4-4-24-4-44-2-2220000-2-2220000−4i4i00000000000000000000000002i−2i−i6i6−i6i66−66−6000000000000000000000000
χ63444-4-4-2-444-4-2-2224-44-422-2-2-2-20000-22200000000004-400000000000000000000000000-220000000000000000
χ64444-4-4-2-444-4-2-2224-44-422-2-2-2-20000-2220000000000-44000000000000000000000000002-20000000000000000
χ65444-4-4-2-444-4-2-222-44-4422-2-22200002-2-20000000000000004-40000000000000000000000000-22000000000000
χ66444-4-4-2-444-4-2-222-44-4422-2-22200002-2-2000000000000000-4400000000000000000000000002-2000000000000
χ6744-44-44-4-4444-44-40000-44-4400000000000000000000000000000000000000000004-400000000000000000000
χ6844-44-44-4-4444-44-40000-44-440000000000000000000000000000000000000000000-4400000000000000000000
χ6944-44-4-244-4-4-22-2244-4-4-22-22-2-2000022-20000000000000000004-40000-2-2220000000000000000000000000000
χ7044-44-4-244-4-4-22-2244-4-4-22-22-2-2000022-2000000000000000000-44000022-2-20000000000000000000000000000
χ7144-44-4-244-4-4-22-22-4-444-22-22220000-2-22000000000000000000004i−4i000000−2i−2i2i2i000000000000000000000000
χ7244-44-4-244-4-4-22-22-4-444-22-22220000-2-2200000000000000000000−4i4i0000002i2i−2i−2i000000000000000000000000
χ7344-4-4444-44-44-4-4400004-4-44004-40000000000000000000400-400000000000000000000000000000000000000
χ7444-4-4444-44-44-4-4400004-4-4400-440000000000000000000-400400000000000000000000000000000000000000
χ7544-4-44-24-44-4-222-20000-222-2004-40000000000000000000-2002000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ7644-4-44-24-44-4-222-20000-222-2004-40000000000000000000-2002000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ7744-4-44-24-44-4-222-20000-222-200-440000000000000000000200-2000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ7844-4-44-24-44-4-222-20000-222-200-440000000000000000000200-2000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ7944-4-44-2-44-44-222-24-4-442-2-22-2-200002-22000000004-400000000000000000000000000-22000000000000000000
χ8044-4-44-2-44-44-222-24-4-442-2-22-2-200002-2200000000-44000000000000000000000000002-2000000000000000000
χ8144-4-44-2-44-44-222-2-444-42-2-22220000-22-20000000000004-400000000000000000000000000-2200000000000000
χ8244-4-44-2-44-44-222-2-444-42-2-22220000-22-2000000000000-44000000000000000000000000002-200000000000000
χ8388888-4-8-8-8-8-4-4-4-40000444400000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-4-8-888-44-4400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-800008000000000004i6−4i6000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-80000800000000000−4i64i6000000000000000000000000000000000000000000000000000000000000000

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