Finite Group Databasebeta

← Group #72271874

Character table — Group #72271874

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222224444444444488888888888888888881212121212121616161616161616161616161616161616242424242424242424242424243232323232323232324848969696
order12222362222224466622244444444666666121222444444666121212121212121212121212222244444444444812121212242424448
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1111111-1-1-1-1111-1-1111-1-1-1-1-11-1-111-1-1-1-1-1-11-11
χ61111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111-1-1111-1-1-1-1-1-111-1-1111111-11-1
χ71111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1111111-1-111-1-1-1-111-11-1
χ81111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-111111-111-1-11111-1-11-11
χ91111111-1-1111111111-11-11-1-1-111-1-111-1-1111111-1-11111-11-11-11111-1-111-1-11-1-1-1-111-1111-1-1-11-1-1-111-1-1111-1-1
χ101111111-1-1111111111-11-11-1-1-111-1-111-1-1111111-1-111-1-1-11-11-1-1-1-1-1-1-111-1-11-1-1-1-111-1111-1-11-1111-1-111-1-1-111
χ111111111-1-1111111111-11-11-1-1-111-1-111-1-11111-1-111-1-111-11-11-11111-1-111-1-1-11111-1-11-1-1-111-11-1-1-111-1-1-1-1-111
χ121111111-1-1111111111-11-11-1-1-111-1-111-1-11111-1-111-1-1-1-1-11-11-1-1-1-1-1-1-111-1-1-11111-1-11-1-1-1111-1111-1-111111-1-1
χ131111111-1-1111111111-1-11-11-1-1-1-11111-1-1111111-1-1-1-111-1-11-111111-1-1-1-1111-1-11111-1-1-1-111-1-11-1-1-1-111-1-111-1
χ141111111-1-1111111111-1-11-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111-11111-1-111-1-11
χ151111111-1-1111111111-1-11-11-1-1-1-11111-1-11111-1-1111111-1-11-111111-1-1-1-111-111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-11
χ161111111-1-1111111111-1-11-11-1-1-1-11111-1-11111-1-11111-1-1-1-11-11-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-111-11111-1-1-1-111-1
χ172222222002-22-2-2-22220202000-2-2002-2002-2-2-22200-2-20002020000000-2-20020000-2-2022-20000000000000000
χ182222222002-22-2-2-22220202000-2-2002-2002-2-2-2-2-200220002020000000-2-200-20000220-2-220000000000000000
χ192222222002-22-2-2-22220-20-200022002-2002-2-2-2220022000-20-20000000220020000-2-20-2-220000000000000000
χ202222222002-22-2-2-22220-20-200022002-2002-2-2-2-2-200-2-2000-20-200000002200-2000022022-20000000000000000
χ21222222200-2-2-2-222222002020000-2-2-2-200-2-222002222000020200000000-2-20-2-2000022-2-20000000000000000
χ22222222200-2-2-2-222222002020000-2-2-2-200-2-22200-2-2-2-2000020200000000-2-20220000-2-2220000000000000000
χ23222222200-2-2-2-22222200-20-2000022-2-200-2-2220022-2-20000-20-200000000220-2-200002-2220000000000000000
χ24222222200-2-2-2-22222200-20-2000022-2-200-2-22200-2-2220000-20-200000000220220000-22-2-20000000000000000
χ25222222222-22-22-2-222220000-2-20000-2222-22-2-200002200200000000-2-20000000-2-2000-22-22200000000000000
χ26222222222-22-22-2-222220000-2-20000-2222-22-2-20000-2-200200000000-2-20000000220002-22-2-200000000000000
χ272222222-2-2-22-22-2-2222-20000220000-22-2-2-22-2-200002200-20000000022000000022000-22-2-2-200000000000000
χ282222222-2-2-22-22-2-2222-20000220000-22-2-2-22-2-20000-2-200-200000000220000000-2-20002-222200000000000000
χ2922222-1-122222222-1-1-122222222222-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000222-1-1-1-1-1-100000
χ3022222-1-122222222-1-1-122222222222-1-1-1-1-1-1-1-1000000-2-2-1-1-1-1-11111-1-1-1-1-1-10000000000000-2-2-211111100000
χ3122222-1-122222222-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-100000022-11111-1-1-1-1-1-1111100000000000002-2-2-1-1111100000
χ3222222-1-122222222-1-1-12-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1000000-2-2-111111111-1-111110000000000000-22211-1-1-1-100000
χ3322222-1-1-2-2222222-1-1-1-22-22-2-2-222-2-2-1-111-1-1-1-1000000221-11-11-1-1-1-111-1-1110000000000000-22-211-1-11100000
χ3422222-1-1-2-2222222-1-1-1-22-22-2-2-222-2-2-1-111-1-1-1-1000000-2-21-11-11111111-1-11100000000000002-22-1-111-1-100000
χ3522222-1-1-2-2222222-1-1-1-2-22-22-2-2-2-222-1-111-1-1-1-10000002211-11-1-1-1-1-11111-1-10000000000000-2-221111-1-100000
χ3622222-1-1-2-2222222-1-1-1-2-22-22-2-2-2-222-1-111-1-1-1-1000000-2-211-11-111111111-1-1000000000000022-2-1-1-1-11100000
χ3722-2-22220022-2-2-22-2-220020-200002-2-2-200222-2220000000020-2000000002-2-2002-22-200002-200000000000000
χ3822-2-22220022-2-2-22-2-220020-200002-2-2-200222-2-2-20000000020-2000000002-2200-22-220000-2200000000000000
χ3922-2-22220022-2-2-22-2-2200-2020000-22-2-200222-22200000000-20200000000-22-200-222-20000-2200000000000000
χ4022-2-22220022-2-2-22-2-2200-2020000-22-2-200222-2-2-200000000-20200000000-222002-2-2200002-200000000000000
χ4122-2-222200-222-22-2-2-22020-20002-2002-200-22-2200220000020-200000002-20002-22-200-2000-2200000000000000
χ4222-2-222200-222-22-2-2-22020-20002-2002-200-22-2200-2-20000020-200000002-2000-22-220020002-200000000000000
χ4322-2-222200-222-22-2-2-220-202000-22002-200-22-22002200000-2020000000-220002-2-2200-20002-200000000000000
χ4422-2-222200-222-22-2-2-220-202000-22002-200-22-2200-2-200000-2020000000-22000-222-2002000-2200000000000000
χ4522-2-2222222-2-222-2-2-22-200002-20000-22222-2-2222220000-2000000002-20000-2-2200-22-20000000000000000000
χ4622-2-2222222-2-222-2-2-22-200002-20000-22222-2-22-2-2-2-20000-2000000002-2000022-2002-220000000000000000000
χ4722-2-222222-2-222-22-2-22-222-2-2-22-22-222222-2-22-200000000-222-2-20000-22-22-22000000000000000000000000000
χ4822-2-222222-2-222-22-2-22-2-2-222-222-22-22222-2-22-200000000-2-2-2220000-222-22-2000000000000000000000000000
χ4922-2-2222-2-22-2-222-2-2-2220000-220000-22-2-22-2-2222-2-20000200000000-220000-22-200-2220000000000000000000
χ5022-2-2222-2-22-2-222-2-2-2220000-220000-22-2-22-2-22-2-2220000200000000-2200002-22002-2-20000000000000000000
χ5122-2-2222-2-2-2-222-22-2-2222-2-222-2-222-222-2-2-2-22-20000000022-2-2200002-2-222-2000000000000000000000000000
χ5222-2-2222-2-2-2-222-22-2-222-222-22-22-2-2222-2-2-2-22-2000000002-222-200002-22-2-22000000000000000000000000000
χ5322-2-22-1-122-2-222-2211-1-222-2-2-22-22-22-1-1-1-111-11000000001-1-11133−3−31-11-11-100000000000000003−33−33−300000
χ5422-2-22-1-122-2-222-2211-1-222-2-2-22-22-22-1-1-1-111-11000000001-1-111−3−3331-11-11-10000000000000000−33−33−3300000
χ5522-2-22-1-122-2-222-2211-1-2-2-222-222-22-2-1-1-1-111-1100000000111-1-133−3−31-1-11-1100000000000000003−3−33−3300000
χ5622-2-22-1-122-2-222-2211-1-2-2-222-222-22-2-1-1-1-111-1100000000111-1-1−3−3331-1-11-110000000000000000−333−33−300000
χ5722-2-22-1-1-2-2-2-222-2211-122-2-222-2-222-2-1-11111-1100000000-1-111-133−3−3-111-1-110000000000000000−333−3−3300000
χ5822-2-22-1-1-2-2-2-222-2211-122-2-222-2-222-2-1-11111-1100000000-1-111-1−3−333-111-1-1100000000000000003−3−333−300000
χ5922-2-22-1-1-2-2-2-222-2211-12-222-22-22-2-22-1-11111-1100000000-11-1-1133−3−3-11-111-10000000000000000−33−333−300000
χ6022-2-22-1-1-2-2-2-222-2211-12-222-22-22-2-22-1-11111-1100000000-11-1-11−3−333-11-111-100000000000000003−33−3−3300000
χ6144444-2-2004-44-4-4-4-2-2-20404000-4-400-2200-2222000000000-20-200000002200000000000000000000000000000
χ6244444-2-2004-44-4-4-4-2-2-20-40-40004400-2200-22220000000002020000000-2-200000000000000000000000000000
χ6344444-2-200-4-4-4-444-2-2-2004040000-4-4220022-2-20000000000-20-20000000022000000000000000000000000000
χ6444444-2-200-4-4-4-444-2-2-200-40-4000044220022-2-2000000000020200000000-2-2000000000000000000000000000
χ6544444-2-244-44-44-4-4-2-2-240000-4-400002-2-2-22-22200000000-200000000220000000000000000000000000000000
χ6644444-2-2-4-4-44-44-4-4-2-2-2-400004400002-2222-22200000000200000000-2-20000000000000000000000000000000
χ67444-4-444000000004-4-4000000000000000000000004i−4i2i−2i000002i−2i2i−2i00000000000000000000000000002-2000
χ68444-4-444000000004-4-4000000000000000000000004i−4i−2i2i00000−2i2i−2i2i0000000000000000000000000000-22000
χ69444-4-444000000004-4-400000000000000000000000−4i4i2i−2i000002i−2i2i−2i0000000000000000000000000000-22000
χ70444-4-444000000004-4-400000000000000000000000−4i4i−2i2i00000−2i2i−2i2i00000000000000000000000000002-2000
χ7144-4-44-2-20044-4-4-4422-20040-400004-42200-2-2-220000000000-20200000000-22000000000000000000000000000
χ7244-4-44-2-20044-4-4-4422-200-4040000-442200-2-2-22000000000020-2000000002-2000000000000000000000000000
χ7344-4-44-2-200-444-44-422-2040-40004-400-22002-22-2000000000-2020000000-2200000000000000000000000000000
χ7444-4-44-2-200-444-44-422-20-404000-4400-22002-22-200000000020-200000002-200000000000000000000000000000
χ7544-4-44-2-2444-4-444-422-2-400004-400002-2-2-2-222-200000000200000000-220000000000000000000000000000000
χ7644-4-44-2-2-4-44-4-444-422-240000-4400002-222-222-200000000-2000000002-20000000000000000000000000000000
χ77888-8-8-4-400000000-44400000000000000000000000004i−4i00000−2i2i−2i2i000000000000000000000000000000000
χ78888-8-8-4-400000000-4440000000000000000000000000−4i4i000002i−2i2i−2i000000000000000000000000000000000
χ7988-88-88800000000-88-8000000000000000000000000000000000000000000000000000000000000000000000
χ8088-88-8-4-4000000004-4400000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ8188-88-8-4-4000000004-44000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ828-80008-84-400000000000000000000004-400004-44-40000000000000000000000000000000000000000000000
χ838-80008-84-400000000000000000000004-40000-44-440000000000000000000000000000000000000000000000
χ848-80008-8-440000000000000000000000-4400004-4-440000000000000000000000000000000000000000000000
χ858-80008-8-440000000000000000000000-440000-444-40000000000000000000000000000000000000000000000
χ8616-16000-888-80000000000000000000000-44000000000000000000000000000000000000000000000000000000
χ8716-16000-88-8800000000000000000000004-4000000000000000000000000000000000000000000000000000000

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