Finite Group Databasebeta

← Group #72271621

Character table — Group #72271621

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222222444444444444488888881212121212121212161616161616161616161616161616161616161616161616242424243232323232323232484848484848484848484848
order122223444466668888121212122424448824242444448888222244441212161616162424484848484848484824886666121212124444888816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111-11-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-11-111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1111-11-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-11111111111111-11-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-11-11-1-111-1-1-1-11111-1-1
χ10111111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111
χ11111111111111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ12111111111111111111111111-1-1-1-111111111111-1-11-11-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-11111-1-111-1-1
χ13111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-11-11-1-1-1-111-1-1-1-1-1-1-1-11111111111-11-11-1-1-1-11111-1-1-1-111
χ14111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1
χ15111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-111-1-1
χ16111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-111111111-1-11-11-11111-1-1-1-111-1-111
χ1722222222222222-2-2-2-22222-2-222-2-2-2-2-22222-2-2-2-200000000220000-2-20000000022-2-200000000000000000000
χ1822222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2222200000000220000-2-200000000-2-22200000000000000000000
χ1922222222222222-2-2-2-22222-2-2-2-222-2-2-22222-2-2-2-200000000-2-200002200000000-2-22200000000000000000000
χ2022222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2222200000000-2-20000220000000022-2-200000000000000000000
χ2122222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-10000000022222222-1-12222-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000
χ2222222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-100000000222-22-2-2-2-1-1-2-2-2-2-1-1111111110000-1-1-11-1111000000000000
χ2322222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-100000000-2-2-22-2222-1-1-2-2-2-2-1-1111111110000111-11-1-1-1000000000000
χ2422222-12222-1-1-1-12222-1-1-1-1-1-12222-1-1-100000000-2-2-2-2-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-1000011111111000000000000
χ2522222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-10000000022-22-22-2-21122-2-2111111-1-1-1-10000-1-11-11-111000000000000
χ2622222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-10000000022-2-2-2-22211-2-22211-1-1-1-111110000-1-11111-1-1000000000000
χ2722222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-100000000-2-22222-2-211-2-22211-1-1-1-11111000011-1-1-1-111000000000000
χ2822222-12222-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-100000000-2-22-22-2221122-2-2111111-1-1-1-1000011-11-11-1-1000000000000
χ29222-2-22-222-222-2-222-2-22-22-2220000-2-222i2i−2i−2i2i2i−2i−2i00020-2000000000000000000000000020-2000000002i−2i0000
χ30222-2-22-222-222-2-222-2-22-22-2220000-2-222i2i−2i−2i2i2i−2i−2i000-2020000000000000000000000000-20200000000−2i2i0000
χ31222-2-22-222-222-2-222-2-22-22-2220000-2-22−2i−2i2i2i−2i−2i2i2i00020-2000000000000000000000000020-200000000−2i2i0000
χ32222-2-22-222-222-2-222-2-22-22-2220000-2-22−2i−2i2i2i−2i−2i2i2i000-2020000000000000000000000000-202000000002i−2i0000
χ33222-2-22-222-222-2-2-2-2222-22-2-2-2000022-22i2i−2i−2i−2i−2i2i2i0000002i−2i000000000000000000000000002i−2i00002-2000000
χ34222-2-22-222-222-2-2-2-2222-22-2-2-2000022-22i2i−2i−2i−2i−2i2i2i000000−2i2i00000000000000000000000000−2i2i0000-22000000
χ35222-2-22-222-222-2-2-2-2222-22-2-2-2000022-2−2i−2i2i2i2i2i−2i−2i0000002i−2i000000000000000000000000002i−2i0000-22000000
χ36222-2-22-222-222-2-2-2-2222-22-2-2-2000022-2−2i−2i2i2i2i2i−2i−2i000000−2i2i00000000000000000000000000−2i2i00002-2000000
χ3722-22-2222-2-22-2-222-22-2-222-22200002-2-22i−2i2i−2i2i−2i2i−2i0000000000002-20022-2-2000000000000000000000000002i−2i
χ3822-22-2222-2-22-2-222-22-2-222-22200002-2-22i−2i2i−2i2i−2i2i−2i000000000000-2200-2-22200000000000000000000000000−2i2i
χ3922-22-2222-2-22-2-222-22-2-222-22200002-2-2−2i2i−2i2i−2i2i−2i2i0000000000002-20022-2-200000000000000000000000000−2i2i
χ4022-22-2222-2-22-2-222-22-2-222-22200002-2-2−2i2i−2i2i−2i2i−2i2i000000000000-2200-2-222000000000000000000000000002i−2i
χ4122-22-2222-2-22-2-22-22-22-222-2-2-20000-2222i−2i2i−2i−2i2i−2i2i00000000002-20000000022-2-2000000000000000000002i−2i00
χ4222-22-2222-2-22-2-22-22-22-222-2-2-20000-2222i−2i2i−2i−2i2i−2i2i0000000000-2200000000-2-22200000000000000000000−2i2i00
χ4322-22-2222-2-22-2-22-22-22-222-2-2-20000-222−2i2i−2i2i2i−2i2i−2i00000000002-20000000022-2-200000000000000000000−2i2i00
χ4422-22-2222-2-22-2-22-22-22-222-2-2-20000-222−2i2i−2i2i2i−2i2i−2i0000000000-2200000000-2-222000000000000000000002i−2i00
χ4522-2-222-22-222-22-22-2-22-2-222220000-22-22-2-222-2-220020-2000000000000000000000000020-2000002-200000000
χ4622-2-222-22-222-22-22-2-22-2-222220000-22-22-2-222-2-2200-2020000000000000000000000000-20200000-2200000000
χ4722-2-222-22-222-22-22-2-22-2-222220000-22-2-222-2-222-20020-2000000000000000000000000020-200000-2200000000
χ4822-2-222-22-222-22-22-2-22-2-222220000-22-2-222-2-222-200-2020000000000000000000000000-202000002-200000000
χ4922-2-222-22-222-22-2-222-2-2-222-2-200002-222-2-22-222-22-2000000000000000000000000002-20000002-20000000000
χ5022-2-222-22-222-22-2-222-2-2-222-2-200002-222-2-22-222-2-2200000000000000000000000000-22000000-220000000000
χ5122-2-222-22-222-22-2-222-2-2-222-2-200002-22-222-22-2-222-2000000000000000000000000002-2000000-220000000000
χ5222-2-222-22-222-22-2-222-2-2-222-2-200002-22-222-22-2-22-2200000000000000000000000000-220000002-20000000000
χ53444444-4-4-4-444440000-4-4-4-4004-40000000000000000000004-400000000000000000000000000000000000000
χ54444444-4-4-4-444440000-4-4-4-400-44000000000000000000000-4400000000000000000000000000000000000000
χ5544444-24444-2-2-2-2-4-4-4-4-2-2-2-22244-4-42220000000000000000-2-200002200000000000000000000000000000000
χ5644444-24444-2-2-2-2-4-4-4-4-2-2-2-222-4-4442220000000000000000220000-2-200000000000000000000000000000000
χ5744444-2-4-4-4-4-2-2-2-200002222004-4000000000000000000000-22000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ5844444-2-4-4-4-4-2-2-2-200002222004-4000000000000000000000-22000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ5944444-2-4-4-4-4-2-2-2-20000222200-440000000000000000000002-2000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ6044444-2-4-4-4-4-2-2-2-20000222200-440000000000000000000002-2000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ61444-4-444-4-4444-4-40000-44-4400000000000000000000000000000000000000000004i−4i00000000000000000000
χ62444-4-444-4-4444-4-40000-44-440000000000000000000000000000000000000000000−4i4i00000000000000000000
χ63444-4-4-2-444-4-2-22244-4-4-22-22-2-2000022-20000000000040-40000000000000000000000000-20200000000000000
χ64444-4-4-2-444-4-2-22244-4-4-22-22-2-2000022-200000000000-404000000000000000000000000020-200000000000000
χ65444-4-4-2-444-4-2-222-4-444-22-22220000-2-22000000000000004i−4i00000000000000000000000000−2i2i000000000000
χ66444-4-4-2-444-4-2-222-4-444-22-22220000-2-2200000000000000−4i4i000000000000000000000000002i−2i000000000000
χ6744-44-44-4-4444-4-4400004-4-4400004-400000000000000000000000004-400000000000000000000000000000000
χ6844-44-44-4-4444-4-4400004-4-440000-440000000000000000000000000-4400000000000000000000000000000000
χ6944-44-4-244-4-4-222-24-44-42-2-22-2-20000-222000000000000000000004-400-2-2220000000000000000000000000000
χ7044-44-4-244-4-4-222-24-44-42-2-22-2-20000-22200000000000000000000-440022-2-20000000000000000000000000000
χ7144-44-4-244-4-4-222-2-44-442-2-222200002-2-20000000000000000004-400000000-2-222000000000000000000000000
χ7244-44-4-244-4-4-222-2-44-442-2-222200002-2-2000000000000000000-440000000022-2-2000000000000000000000000
χ7344-44-4-2-4-444-222-20000-222-200004-40000000000000000000000000-22i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ7444-44-4-2-4-444-222-20000-222-200004-40000000000000000000000000-22−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ7544-44-4-2-4-444-222-20000-222-20000-4400000000000000000000000002-2i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ7644-44-4-2-4-444-222-20000-222-20000-4400000000000000000000000002-2−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ7744-4-4444-44-44-44-4000044-4-4000000000000000000000000000000000000000004-40000000000000000000000
χ7844-4-4444-44-44-44-4000044-4-400000000000000000000000000000000000000000-440000000000000000000000
χ7944-4-44-2-44-44-22-224-4-4422-2-2-2-200002-22000000000040-40000000000000000000000000-202000000000000000
χ8044-4-44-2-44-44-22-224-4-4422-2-2-2-200002-220000000000-404000000000000000000000000020-2000000000000000
χ8144-4-44-2-44-44-22-22-444-422-2-2220000-22-2000000004-400000000000000000000000000-22000000000000000000
χ8244-4-44-2-44-44-22-22-444-422-2-2220000-22-200000000-44000000000000000000000000002-2000000000000000000
χ83888-8-8-48-8-88-4-44400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-48-88-8-44-440000-4-44400000000000000000000000000000000000000000000000000000000000000000
χ8516-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-800008000000000004i6−4i6000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-80000800000000000−4i64i6000000000000000000000000000000000000000000000000000000000000000

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