Finite Group Databasebeta

← Group #72271920

Character table — Group #72271920

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222244444444444448888888888888888888888121212121616161616161616162424242424242424242424242424323232323232323232323232484848489696
order122223622222244446662244444444666666121212121212224466121212121212122222244444444444881212121224242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111-1-1111111-1-111-1-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-1111-1-1-1-1111-1-1-1-11-11-111-1-111-1-111-1-11-1
χ61111111111111-1-1111111-1-111-1-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-1111-1-1-1-1111-1-1-1-1-11-11-1-111-1-111-1-111-11
χ71111111111111-1-1111111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-11-1-111-1-1-1-1-1-1-11111-1-1-111111-11-111-1-111-1-1-1-111-11
χ81111111111111-1-1111111-1-111-1-1-1-1-1111111-1-1-1-111-1-1-1-11-1-111-1-1-1-1-1-1-11111-1-1-11111-11-11-1-111-1-11111-1-11-1
χ91111111-1-111111111111-1-1-1-1-1111-1-111-1-11111111111-1-1-1-1-1-1-111-1-11-1-11-11-111-111-1-111-1-11111-1-1-1-11111-1-1
χ101111111-1-111111111111-1-1-1-1-1111-1-111-1-11111111111-1-1-1-1-1-1-111-1-11-1-11-11-111-111-1-1-1-111-1-1-1-11111-1-1-1-111
χ111111111-1-111111111111-1-1-1-1-1111-1-111-1-111111111-1-111-1-1-1-1-111-1-1-111-11-11-1-11-1-11111-1-11111-1-1-1-1-1-1-1-111
χ121111111-1-111111111111-1-1-1-1-1111-1-111-1-111111111-1-111-1-1-1-1-111-1-1-111-11-11-1-11-1-111-1-111-1-1-1-111111111-1-1
χ131111111-1-11111-1-111111-111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-111-1-1-1-1111-1-1-11-1111-1-1-1111-1-1111-1-1-1-11111-1-1-11
χ141111111-1-11111-1-111111-111-1-1-1-1-11111-1-111-1-1-1-11111-1-1-111-1-1-1-1111-1-1-11-1111-1-1-111-111-1-1-11111-1-1-1-1111-1
χ151111111-1-11111-1-111111-111-1-1-1-1-11111-1-111-1-1-1-111-1-111-111-1-1-1-111-1111-11-1-1-1111-1-11-1-1111-1-1-1-111-1-1111-1
χ161111111-1-11111-1-111111-111-1-1-1-1-11111-1-111-1-1-1-111-1-111-111-1-1-1-111-1111-11-1-1-1111-1-1-111-1-1-11111-1-111-1-1-11
χ1722222220022-2-222-2-2222000002-2-200-2-2002222-2-2-2-22200000002-200200-20-20-2-202200000000000000000000
χ1822222220022-2-222-2-2222000002-2-200-2-2002222-2-2-2-2-2-200000002-200-2002020220-2-200000000000000000000
χ1922222220022-2-2-2-2-2-222200000-22200-2-20022-2-222-2-2220000000-22002002020-2-20-2-200000000000000000000
χ2022222220022-2-2-2-2-2-222200000-22200-2-20022-2-222-2-2-2-20000000-2200-200-20-202202200000000000000000000
χ21222222200-2-2-2-2222222200000-22-200-2-200-2-222-2-222002200000-22000-2-2020200200-2-2000000000000000000
χ22222222200-2-2-2-2222222200000-22-200-2-200-2-222-2-22200-2-200000-22000220-20-200-20022000000000000000000
χ23222222200-2-2-2-2-2-222222000002-2200-2-200-2-2-2-222220022000002-2000-2-20-20-20020022000000000000000000
χ24222222200-2-2-2-2-2-222222000002-2200-2-200-2-2-2-2222200-2-2000002-200022020200-200-2-2000000000000000000
χ25222222222-2-22222-2-22222-2-2-2-2-2-22222222-2-22222-2-200002-2-2-2-2-2-22200000000000000000000000000000000
χ26222222222-2-222-2-2-2-2222222-2-222-2-2-22222-2-2-2-2-2-2-2-20000222-2-222-2-200000000000000000000000000000000
χ272222222-2-2-2-22222-2-2222-22222-2-22-2-222-2-2-2-22222-2-20000-22222-2-2-2-200000000000000000000000000000000
χ282222222-2-2-2-222-2-2-2-2222-2-2-22222-22222-2-2-2-2-2-2-2-2-2-20000-2-2-222222200000000000000000000000000000000
χ2922222-1-12222222222-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1000000000000002222-1-1-1-1-1-1-1-1000000
χ3022222-1-12222222222-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-100000000000000-2-2-2-211111111000000
χ3122222-1-1222222-2-222-1-1-12-2-222-2-2-2-2-2-1-1-1-1-1-11111-1-10000-111-1-11111000000000000002-22-2-1-111-1-111000000
χ3222222-1-1222222-2-222-1-1-12-2-222-2-2-2-2-2-1-1-1-1-1-11111-1-10000-111-1-1111100000000000000-22-2211-1-111-1-1000000
χ3322222-1-122-2-22222-2-2-1-1-12-2-2-2-2-2-2222-1-1-1-111-1-1-1-1110000-1111111-1-10000000000000000003−33−33−33−3000000
χ3422222-1-122-2-22222-2-2-1-1-12-2-2-2-2-2-2222-1-1-1-111-1-1-1-1110000-1111111-1-1000000000000000000−33−33−33−33000000
χ3522222-1-122-2-222-2-2-2-2-1-1-1222-2-222-2-2-2-1-1-1-1111111110000-1-1-111-1-1110000000000000000003−3−333−3−33000000
χ3622222-1-122-2-222-2-2-2-2-1-1-1222-2-222-2-2-2-1-1-1-1111111110000-1-1-111-1-111000000000000000000−333−3−333−3000000
χ3722222-1-1-2-222222222-1-1-1-2-2-2-2-2222-2-2-1-111-1-1-1-1-1-1-1-1000011111-1-1110000000000000022-2-2-1-1-1-11111000000
χ3822222-1-1-2-222222222-1-1-1-2-2-2-2-2222-2-2-1-111-1-1-1-1-1-1-1-1000011111-1-11100000000000000-2-2221111-1-1-1-1000000
χ3922222-1-1-2-22222-2-222-1-1-1-222-2-2-2-2-222-1-111-1-11111-1-100001-1-11111-1-1000000000000002-2-22-1-11111-1-1000000
χ4022222-1-1-2-22222-2-222-1-1-1-222-2-2-2-2-222-1-111-1-11111-1-100001-1-11111-1-100000000000000-222-211-1-1-1-111000000
χ4122222-1-1-2-2-2-22222-2-2-1-1-1-22222-2-22-2-2-1-11111-1-1-1-11100001-1-1-1-111110000000000000000003−33−3−33−33000000
χ4222222-1-1-2-2-2-22222-2-2-1-1-1-22222-2-22-2-2-1-11111-1-1-1-11100001-1-1-1-11111000000000000000000−33−333−33−3000000
χ4322222-1-1-2-2-2-222-2-2-2-2-1-1-1-2-2-22222-222-1-111111111110000111-1-1-1-1-1-10000000000000000003−3−33−333−3000000
χ4422222-1-1-2-2-2-222-2-2-2-2-1-1-1-2-2-22222-222-1-111111111110000111-1-1-1-1-1-1000000000000000000−333−33−3−33000000
χ4522-2-2222002-22-2002-2-2-2202-2000002-22-2002-200002-2002202-200002-202-220-2000-22-200000000000000000000
χ4622-2-2222002-22-2002-2-2-2202-2000002-22-2002-200002-200-2-202-200002-20-22-2020002-2200000000000000000000
χ4722-2-2222002-22-2002-2-2-220-2200000-222-2002-200002-200220-220000-2202-2-202000-2-2200000000000000000000
χ4822-2-2222002-22-2002-2-2-220-2200000-222-2002-200002-200-2-20-220000-220-2220-200022-200000000000000000000
χ4922-2-222200-222-200-22-2-2202-200000-222-200-220000-22220002-20000-22-200020-22-20002-2000000000000000000
χ5022-2-222200-222-200-22-2-2202-200000-222-200-220000-22-2-20002-20000-222000-202-22000-22000000000000000000
χ5122-2-222200-222-200-22-2-220-22000002-22-200-220000-2222000-2200002-2-2000-2022-2000-22000000000000000000
χ5222-2-222200-222-200-22-2-220-22000002-22-200-220000-22-2-2000-2200002-2200020-2-220002-2000000000000000000
χ5322-2-2222222-2-2200-22-2-22-2002-200000-22222-20000-220000-2002-2000000022-2-2000-22-22000000000000000000
χ5422-2-2222222-2-2200-22-2-22-2002-200000-22222-20000-220000-2002-20000000-2-2220002-22-2000000000000000000
χ5522-2-222222-22-22002-2-2-22-200-2200000-2222-2200002-22222-200-220000-2-220000-22-20000000000000000000000
χ5622-2-222222-22-22002-2-2-22-200-2200000-2222-2200002-2-2-2-2-2-200-22000022-200002-220000000000000000000000
χ5722-2-2222-2-22-2-2200-22-2-22200-2200000-22-2-22-20000-220000200-2200000002-2-22000-222-2000000000000000000
χ5822-2-2222-2-22-2-2200-22-2-22200-2200000-22-2-22-20000-220000200-220000000-222-20002-2-22000000000000000000
χ5922-2-2222-2-2-22-22002-2-2-222002-200000-22-2-2-2200002-222-2-22002-20000-22-20000-2220000000000000000000000
χ6022-2-2222-2-2-22-22002-2-2-222002-200000-22-2-2-2200002-2-2-2222002-200002-2200002-2-20000000000000000000000
χ6144444-2-20044-4-444-4-4-2-2-2000004-4-4002200-2-2-2-22222000000000-220000000000000000000000000000000000
χ6244444-2-20044-4-4-4-4-4-4-2-2-200000-444002200-2-222-2-2220000000002-20000000000000000000000000000000000
χ6344444-2-200-4-4-4-44444-2-2-200000-44-400220022-2-222-2-20000000002-20000000000000000000000000000000000
χ6444444-2-200-4-4-4-4-4-444-2-2-2000004-440022002222-2-2-2-2000000000-220000000000000000000000000000000000
χ65444-4-4440000004i−4i004-4-400000000000000004i−4i00000000000000000000000000000000000000000002-22i−2i00
χ66444-4-4440000004i−4i004-4-400000000000000004i−4i0000000000000000000000000000000000000000000-22−2i2i00
χ67444-4-444000000−4i4i004-4-40000000000000000−4i4i00000000000000000000000000000000000000000002-2−2i2i00
χ68444-4-444000000−4i4i004-4-40000000000000000−4i4i0000000000000000000000000000000000000000000-222i−2i00
χ6944-4-44-2-2004-44-4004-422-204-4000004-4-2200-220000-2200000-220000-2200000000000000000000000000000000
χ7044-4-44-2-2004-44-4004-422-20-4400000-44-2200-220000-22000002-200002-200000000000000000000000000000000
χ7144-4-44-2-200-444-400-4422-204-400000-44-22002-200002-200000-2200002-200000000000000000000000000000000
χ7244-4-44-2-200-444-400-4422-20-44000004-4-22002-200002-2000002-20000-2200000000000000000000000000000000
χ7344-4-44-2-2444-4-4400-4422-2-4004-4000002-2-2-2-2200002-20000200-22000000000000000000000000000000000000
χ7444-4-44-2-244-44-44004-422-2-400-44000002-2-2-22-20000-2200002002-2000000000000000000000000000000000000
χ7544-4-44-2-2-4-44-4-4400-4422-2400-44000002-222-2200002-20000-2002-2000000000000000000000000000000000000
χ7644-4-44-2-2-4-4-44-44004-422-24004-4000002-2222-20000-220000-200-22000000000000000000000000000000000000
χ77888-8-8-4-40000008i−8i00-4440000000000000000−4i4i0000000000000000000000000000000000000000000000000
χ78888-8-8-4-4000000−8i8i00-44400000000000000004i−4i0000000000000000000000000000000000000000000000000
χ7988-88-8880000000000-88-80000000000000000000000000000000000000000000000000000000000000000000
χ8088-88-8-4-400000000004-4400000000000000000043−4300000000000000000000000000000000000000000000000
χ8188-88-8-4-400000000004-44000000000000000000−434300000000000000000000000000000000000000000000000
χ828-80008-84-4000000000000000000000004-4000000004-44-400000000000000000000000000000000000000000
χ838-80008-84-4000000000000000000000004-400000000-44-4400000000000000000000000000000000000000000
χ848-80008-8-4400000000000000000000000-44000000004-4-4400000000000000000000000000000000000000000
χ858-80008-8-4400000000000000000000000-4400000000-444-400000000000000000000000000000000000000000
χ8616-16000-888-800000000000000000000000-4400000000000000000000000000000000000000000000000000000
χ8716-16000-88-88000000000000000000000004-400000000000000000000000000000000000000000000000000000

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