Finite Group Databasebeta

← Group #72271866

Character table — Group #72271866

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222224444444444488888888888888888881212121212121616161616161616161616161616161616242424242424242424242424243232323232323232324848969696
order122223622224444666222244444446666121212122222444466661212121212121212121212222444444444444812121212242424448
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-11-1-1-1-1111111111111-1-11111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-1-1-111-1-111-1
χ611111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-111-11111-1-111-1-11
χ711111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111111-1-11-1-1-1-11111-1-11
χ811111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111111-11111-1-1-1-111-1
χ911111111111-1-111111-1-11-11-1-111-1-111111-1-1111-1-11111-1-11-11-11111-111-1-11-1-1-111-1-1111-1-11-1-111-1-1-1-1111-1-1
χ1011111111111-1-111111-1-11-11-1-111-1-111111-1-1111-1-111-1-1-1-11-11-1-1-1-1-1-111-1-11-1-1-111-1-1111-1-1-111-1-11111-1-1-111
χ1111111111111-1-111111-1-11-11-1-111-1-111111-1-11-1-111-1-111-1-11-11-11111-111-1-1-1111-1-111-1-1-1111-1-111-1-1-1-1-1-1-111
χ1211111111111-1-111111-1-11-11-1-111-1-111111-1-11-1-111-1-1-1-1-1-11-11-1-1-1-1-1-111-1-1-1111-1-111-1-1-111-111-1-11111111-1-1
χ1311111111111-1-111111-1-1-11-11-1-1-11111111-1-1111-1-1-1-111-1-1-11-111111-1-1-1111-11111-1-1-1-1-111-11-1-1-111-1-1-1-11-11
χ1411111111111-1-111111-1-1-11-11-1-1-11111111-1-1111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1111-11111-1-1-1-1-1111-1111-1-11111-11-1
χ1511111111111-1-111111-1-1-11-11-1-1-11111111-1-11-1-1111111-1-1-11-111111-1-1-111-11-1-1-1-111111-1-1-11-1-1-111-1-111-11-1
χ1611111111111-1-111111-1-1-11-11-1-1-11111111-1-11-1-11111-1-1-1-1-11-11-1-1-1-1-1-1-111-11-1-1-1-111111-1-11-1111-1-111-1-11-11
χ1722222222-22-200-2-2222000202000-2-22-22-2-200-20022-2-2000002020000000-2-2020000-2-222-20000000000000000
χ1822222222-22-200-2-2222000202000-2-22-22-2-200-200-2-222000002020000000-2-20-2000022-2-220000000000000000
χ1922222222-22-200-2-2222000-20-2000222-22-2-200-200222200000-20-2000000022020000-2-2-2-220000000000000000
χ2022222222-22-200-2-2222000-20-2000222-22-2-200-200-2-2-2-200000-20-20000000220-200002222-20000000000000000
χ212222222-22-2200-2-22220020200-2-200-22-22-200-22200-2-20000202000000-2-2002000-2-2002-220000000000000000
χ222222222-22-2200-2-22220020200-2-200-22-22-200-2-2-200220000202000000-2-200-20002200-22-20000000000000000
χ232222222-22-2200-2-222200-20-2002200-22-22-200-22200220000-20-200000022002000-2-200-22-20000000000000000
χ242222222-22-2200-2-222200-20-2002200-22-22-200-2-2-200-2-20000-20-20000002200-200022002-220000000000000000
χ252222222-2-2-2-22222222-2-2000020000-2-2-2-2222200002200-2-20000000020000002200002-2-2-2-200000000000000
χ262222222-2-2-2-22222222-2-2000020000-2-2-2-222220000-2-200-2-2000000002000000-2-20000-2222200000000000000
χ272222222-2-2-2-2-2-222222220000-20000-2-2-2-22-2-22000022002200000000-2000000-2-200002-2-22200000000000000
χ282222222-2-2-2-2-2-222222220000-20000-2-2-2-22-2-220000-2-2002200000000-2000000220000-222-2-200000000000000
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
χ3022222-1-122222222-1-1-122222222222-1-1-1-1-1-1-1-1000000-2-2-1-1-1-1-1-11111-1-1-1-1-10000000000000-2-2-211111100000
χ3122222-1-122222222-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-100000022-1-11111-1-1-1-1-111110000000000000-2-221111-1-100000
χ3222222-1-122222222-1-1-122-2-2-2-22-2-2-2-2-1-1-1-1-1-1-1-1000000-2-2-1-111111111-11111000000000000022-2-1-1-1-11100000
χ3322222-1-12222-2-222-1-1-1-2-22-22-2-222-2-2-1-1-1-1-111-10000002211-11-11-1-1-1-11-1-11100000000000002-2-2-1-1111100000
χ3422222-1-12222-2-222-1-1-1-2-22-22-2-222-2-2-1-1-1-1-111-1000000-2-211-11-1111111-1-1110000000000000-22211-1-1-1-100000
χ3522222-1-12222-2-222-1-1-1-2-2-22-22-2-2-222-1-1-1-1-111-100000022111-11-1-1-1-1-1111-1-10000000000000-22-211-1-11100000
χ3622222-1-12222-2-222-1-1-1-2-2-22-22-2-2-222-1-1-1-1-111-1000000-2-2111-11-11111111-1-100000000000002-22-1-111-1-100000
χ3722-2-222222-2-222-22-2-222-20000-20000-2-222222-2222200002-200000000-20000-2-2002-22-20000000000000000000
χ3822-2-222222-2-222-22-2-222-20000-20000-2-222222-2-2-2-2-200002-200000000-200002200-22-220000000000000000000
χ3922-2-222222-2-2-2-2-22-2-22-22000020000-2-2222-2-2-222-2-20000-220000000020000-22002-2-220000000000000000000
χ4022-2-222222-2-2-2-2-22-2-22-22000020000-2-2222-2-2-2-2-2220000-2200000000200002-200-222-20000000000000000000
χ4122-2-22222-2-22002-2-2-220020-2002-200-222-2-2002002200000020-20000002-2000-22-200-220002-200000000000000
χ4222-2-22222-2-22002-2-2-220020-2002-200-222-2-200200-2-200000020-20000002-20002-22002-2000-2200000000000000
χ4322-2-22222-2-22002-2-2-2200-20200-2200-222-2-20020022000000-202000000-22000-2-2200-22000-2200000000000000
χ4422-2-22222-2-22002-2-2-2200-20200-2200-222-2-200200-2-2000000-202000000-2200022-2002-20002-200000000000000
χ4522-2-2222-222-2002-2-2-2200020-20002-22-2-22-20022200000000020-200000002-2-202-2-2200000-2200000000000000
χ4622-2-2222-222-2002-2-2-2200020-20002-22-2-22-2002-2-200000000020-200000002-220-222-2000002-200000000000000
χ4722-2-2222-222-2002-2-2-22000-202000-222-2-22-200222000000000-2020000000-22-20-22-22000002-200000000000000
χ4822-2-2222-222-2002-2-2-22000-202000-222-2-22-2002-2-2000000000-2020000000-22202-22-200000-2200000000000000
χ4922-2-2222-2-22222-22-2-22-2222-2-2-2-22-2222-2-2222-200000000-2222-2-20000-2-22-22000000000000000000000000000
χ5022-2-2222-2-22222-22-2-22-22-2-222-22-22-222-2-2222-200000000-22-2-2220000-22-22-2000000000000000000000000000
χ5122-2-2222-2-222-2-2-22-2-222-22-2-222-222-222-2-22-2-2-2000000002-22-2-2200002-222-2000000000000000000000000000
χ5222-2-2222-2-222-2-2-22-2-222-2-222-222-2-2222-2-22-2-2-2000000002-2-222-2000022-2-22000000000000000000000000000
χ5322-2-22-1-1-2-22222-2211-1-2222-2-2-2-22-22-1-111-1-1-11000000001-1-1-11133−3−311-11-100000000000000003−33−33−300000
χ5422-2-22-1-1-2-22222-2211-1-2222-2-2-2-22-22-1-111-1-1-11000000001-1-1-111−3−33311-11-10000000000000000−33−33−3300000
χ5522-2-22-1-1-2-22222-2211-1-22-2-222-22-22-2-1-111-1-1-11000000001-111-1-133−3−31-11-110000000000000000−33−333−300000
χ5622-2-22-1-1-2-22222-2211-1-22-2-222-22-22-2-1-111-1-1-11000000001-111-1-1−3−3331-11-1100000000000000003−33−3−3300000
χ5722-2-22-1-1-2-222-2-2-2211-12-22-2-222-222-2-1-111-111100000000-11-111-133−3−3-11-1-1100000000000000003−3−33−3300000
χ5822-2-22-1-1-2-222-2-2-2211-12-22-2-222-222-2-1-111-111100000000-11-111-1−3−333-11-1-110000000000000000−333−33−300000
χ5922-2-22-1-1-2-222-2-2-2211-12-2-222-222-2-22-1-111-111100000000-111-1-1133−3−3-1-111-10000000000000000−333−3−3300000
χ6022-2-22-1-1-2-222-2-2-2211-12-2-222-222-2-22-1-111-111100000000-111-1-11−3−333-1-111-100000000000000003−3−333−300000
χ6144444-2-24-44-400-4-4-2-2-2000404000-4-4-22-22200200000000000-20-2000000022000000000000000000000000000
χ6244444-2-24-44-400-4-4-2-2-2000-40-400044-22-222002000000000002020000000-2-2000000000000000000000000000
χ6344444-2-2-44-4400-4-4-2-2-20040400-4-4002-22-220020000000000-20-20000002200000000000000000000000000000
χ6444444-2-2-44-4400-4-4-2-2-200-40-40044002-22-220020000000000202000000-2-200000000000000000000000000000
χ6544444-2-2-4-4-4-44444-2-2-2-4-40000400002222-2-2-2-2000000002200000000-20000000000000000000000000000000
χ6644444-2-2-4-4-4-4-4-444-2-2-2440000-400002222-222-200000000-2-20000000020000000000000000000000000000000
χ67444-4-444000000004-4-4000000000000000000000004i−4i2i−2i0000002i−2i2i−2i0000000000000000000000000002-2000
χ68444-4-444000000004-4-4000000000000000000000004i−4i−2i2i000000−2i2i−2i2i000000000000000000000000000-22000
χ69444-4-444000000004-4-400000000000000000000000−4i4i2i−2i0000002i−2i2i−2i000000000000000000000000000-22000
χ70444-4-444000000004-4-400000000000000000000000−4i4i−2i2i000000−2i2i−2i2i0000000000000000000000000002-2000
χ7144-4-44-2-244-4-444-4422-24-40000-4000022-2-2-2-2-2200000000-220000000020000000000000000000000000000000
χ7244-4-44-2-244-4-4-4-4-4422-2-4400004000022-2-2-2222000000002-200000000-20000000000000000000000000000000
χ7344-4-44-2-24-4-44004-422-20040-4004-4002-2-22200-20000000000-202000000-2200000000000000000000000000000
χ7444-4-44-2-24-4-44004-422-200-40400-44002-2-22200-2000000000020-20000002-200000000000000000000000000000
χ7544-4-44-2-2-444-4004-422-200040-40004-4-222-2200-200000000000-2020000000-22000000000000000000000000000
χ7644-4-44-2-2-444-4004-422-2000-404000-44-222-2200-20000000000020-200000002-2000000000000000000000000000
χ77888-8-8-4-400000000-44400000000000000000000000004i−4i000000−2i2i−2i2i00000000000000000000000000000000
χ78888-8-8-4-400000000-4440000000000000000000000000−4i4i0000002i−2i2i−2i00000000000000000000000000000000
χ7988-88-88800000000-88-8000000000000000000000000000000000000000000000000000000000000000000000
χ8088-88-8-4-4000000004-44000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ8188-88-8-4-4000000004-440000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ828-80008-800004-40000000000000000000004-404-44-40000000000000000000000000000000000000000000000
χ838-80008-800004-40000000000000000000004-40-44-440000000000000000000000000000000000000000000000
χ848-80008-80000-44000000000000000000000-4404-4-440000000000000000000000000000000000000000000000
χ858-80008-80000-44000000000000000000000-440-444-40000000000000000000000000000000000000000000000
χ8616-16000-8800008-8000000000000000000000-44000000000000000000000000000000000000000000000000000
χ8716-16000-880000-880000000000000000000004-4000000000000000000000000000000000000000000000000000

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