Finite Group Databasebeta

← Group #72271746

Character table — Group #72271746

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444888888888888161616161616161616161616161616161616161616161616161624242424242424243232323232324848484896969696
order1222222222366622226666662244666612121212244444446666121212121212121212121212121222224444882424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ92222222222222222-2-22222222-2-2-222-2-2-2-2-2-2000000002-200000000000000000000222200000000-2-20000
χ102222222222222222-2-22222222-2-2-222-2-2-2-2-2-2000000002-200000000000000000000-2-2-2-200000000220000
χ1122222222222222-2-222222222-22-2-2-2-222-2-2-2-200000000-22000000000000000022220000000000-2-2000000
χ1222222222222222-2-222222222-22-2-2-2-222-2-2-2-200000000-220000000000000000-2-2-2-2000000000022000000
χ1322222222222222-2-2-2-2222222-2-222-2-2-2-22222000022-2-2-2-2000000002222-2-2-2-20000000000000000000000
χ1422222222222222-2-2-2-2222222-2-222-2-2-2-222220000-2-222-2-200000000-2-2-2-222220000000000000000000000
χ152222222222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-100000000
χ162222222222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-2111100000000
χ172222222222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-2111100000000
χ182222222222-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-100000000
χ192222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2221111-1-1-1-1000022-2-211−i3i3−i3−i3i3i3−i3i3-1-1-1-111110000000000−i3−i3i3i300000000
χ202222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2221111-1-1-1-1000022-2-211i3−i3i3i3−i3−i3i3−i3-1-1-1-111110000000000i3i3−i3−i300000000
χ212222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2221111-1-1-1-10000-2-22211−i3i3−i3−i3i3i3−i3i31111-1-1-1-10000000000i3i3−i3−i300000000
χ222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-2-2221111-1-1-1-10000-2-22211i3−i3i3i3−i3−i3i3−i31111-1-1-1-10000000000−i3−i3i3i300000000
χ2322222-2-2-2-222222222222-2-2-2-2-2-22-2222222-2-22-22-20000-2-222-2-2-2-222000000000000000000000000000000
χ2422222-2-2-2-222222222222-2-2-2-2-2-22-2222222-2-2-22-220000-2-2-2-22222-2-2000000000000000000000000000000
χ2522222-2-2-2-22222222-2-222-2-2-2-2-22-2222-2-2-2-22200000000-220000000000000000000000000000000000002-2
χ2622222-2-2-2-22222222-2-222-2-2-2-2-22-2222-2-2-2-22200000000-22000000000000000000000000000000000000-22
χ2722222-2-2-2-222222-2-22222-2-2-2-22-2-22-2-222-2-222000000002-200000000000000000000000000000000002-200
χ2822222-2-2-2-222222-2-22222-2-2-2-22-2-22-2-222-2-222000000002-20000000000000000000000000000000000-2200
χ2922222-2-2-2-222222-2-2-2-222-2-2-2-2222-2-2-2-2-222-2-200000000220000000000000000000000002i−2i2i−2i2i−2i00000000
χ3022222-2-2-2-222222-2-2-2-222-2-2-2-2222-2-2-2-2-222-2-20000000022000000000000000000000000−2i2i−2i2i−2i2i00000000
χ3122222-2-2-2-22-1-1-1-12222-1-11111-2-22-2-1-1-1-1-1-1112-22-2000011-1-11111-1-133−3−333−3−300000000003−3−3300000000
χ3222222-2-2-2-22-1-1-1-12222-1-11111-2-22-2-1-1-1-1-1-1112-22-2000011-1-11111-1-1−3−333−3−3330000000000−333−300000000
χ3322222-2-2-2-22-1-1-1-12222-1-11111-2-22-2-1-1-1-1-1-111-22-2200001111-1-1-1-11133−3−333−3−30000000000−333−300000000
χ3422222-2-2-2-22-1-1-1-12222-1-11111-2-22-2-1-1-1-1-1-111-22-2200001111-1-1-1-111−3−333−3−33300000000003−3−3300000000
χ3522222-2-2-2-22-1-1-1-1-2-2-2-2-1-11111222-21111-1-11100000000-1-1−i3i3i3i3−i3−i3−i3i333−3−3−3−333000000002i−2i−ii−ii00000000
χ3622222-2-2-2-22-1-1-1-1-2-2-2-2-1-11111222-21111-1-11100000000-1-1−i3i3i3i3−i3−i3−i3i3−3−33333−3−300000000−2i2ii−ii−i00000000
χ3722222-2-2-2-22-1-1-1-1-2-2-2-2-1-11111222-21111-1-11100000000-1-1i3−i3−i3−i3i3i3i3−i333−3−3−3−33300000000−2i2ii−ii−i00000000
χ3822222-2-2-2-22-1-1-1-1-2-2-2-2-1-11111222-21111-1-11100000000-1-1i3−i3−i3−i3i3i3i3−i3−3−33333−3−3000000002i−2i−ii−ii00000000
χ394444444444-2-2-2-244-4-4-2-2-2-2-2-24-4-4-4-2-222222200000000-2200000000000000000000000000000000000000
χ404444444444-2-2-2-2-4-444-2-2-2-2-2-2-44-4-422-2-22222000000002-200000000000000000000000000000000000000
χ4144444-4-4-4-44-2-2-2-244-4-4-2-22222-44-44-2-22222-2-2000000002-200000000000000000000000000000000000000
χ4244444-4-4-4-44-2-2-2-2-4-444-2-222224-4-4422-2-222-2-200000000-2200000000000000000000000000000000000000
χ434444-44-44-4-444440000-4-44-44-400000000000022-2-2000000222-22-2-2-2000000000000000000000000000000
χ444444-44-44-4-444440000-4-44-44-4000000000000-2-222000000-2-2-22-2222000000000000000000000000000000
χ454444-44-44-4-4-2-2-2-2000022-22-2200000000−2i32i3−2i32i322-2-2000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i3000000000000000000000000000000
χ464444-44-44-4-4-2-2-2-2000022-22-2200000000−2i32i3−2i32i3-2-2220000001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i3000000000000000000000000000000
χ474444-44-44-4-4-2-2-2-2000022-22-22000000002i3−2i32i3−2i322-2-2000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i3000000000000000000000000000000
χ484444-44-44-4-4-2-2-2-2000022-22-22000000002i3−2i32i3−2i3-2-2220000001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i3000000000000000000000000000000
χ494444-4-44-44-444440000-4-4-44-440000000000002-2-2200000022-22-22-2-2000000000000000000000000000000
χ504444-4-44-44-444440000-4-4-44-44000000000000-222-2000000-2-22-22-222000000000000000000000000000000
χ514444-4-44-44-4-2-2-2-20000222-22-200000000−2i32i32i3−2i32-2-22000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i3000000000000000000000000000000
χ524444-4-44-44-4-2-2-2-20000222-22-200000000−2i32i32i3−2i3-222-20000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000000000000000000000
χ534444-4-44-44-4-2-2-2-20000222-22-2000000002i3−2i3−2i32i32-2-22000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i3000000000000000000000000000000
χ544444-4-44-44-4-2-2-2-20000222-22-2000000002i3−2i3−2i32i3-222-20000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000000000000000000000
χ5544-4-4040-40044-4-400000040-400000000000000000002i−2i000000000000002i−2i2i−2i22-2-22i2i−2i−2i00000000000000
χ5644-4-4040-40044-4-400000040-400000000000000000002i−2i000000000000002i−2i2i−2i-2-222−2i−2i2i2i00000000000000
χ5744-4-4040-40044-4-400000040-40000000000000000000−2i2i00000000000000−2i2i−2i2i22-2-2−2i−2i2i2i00000000000000
χ5844-4-4040-40044-4-400000040-40000000000000000000−2i2i00000000000000−2i2i−2i2i-2-2222i2i−2i−2i00000000000000
χ594-44-440000-44-4-44004-44-400000000004-400000000000000000000000000000000002i−2i2i−2i000000002i−2i0000
χ604-44-440000-44-4-44004-44-400000000004-40000000000000000000000000000000000−2i2i−2i2i00000000−2i2i0000
χ614-44-440000-44-4-4400-444-40000000000-4400000000000000000000000000000000002i−2i2i−2i00000000−2i2i0000
χ624-44-440000-44-4-4400-444-40000000000-440000000000000000000000000000000000−2i2i−2i2i000000002i−2i0000
χ634-44-4-4000044-4-444-400-44000000004-4000000000000000000000000000000002-22-200000000002-2000000
χ644-44-4-4000044-4-444-400-44000000004-400000000000000000000000000000000-22-220000000000-22000000
χ654-44-4-4000044-4-44-4400-4400000000-44000000000000000000000000000000002-22-20000000000-22000000
χ664-44-4-4000044-4-44-4400-4400000000-4400000000000000000000000000000000-22-2200000000002-2000000
χ674-4-4400-40404-44-40000000-40400000000000000002-20000000000002-22-200002-2-222-2-2200000000000000
χ684-4-4400-40404-44-40000000-40400000000000000002-20000000000002-22-20000-222-2-222-200000000000000
χ694-4-4400-40404-44-40000000-4040000000000000000-22000000000000-22-2200002-2-22-222-200000000000000
χ704-4-4400-40404-44-40000000-4040000000000000000-22000000000000-22-220000-222-22-2-2200000000000000
χ7188-8-8080-800-4-444000000-40400000000000000000004i−4i00000000000000−2i2i−2i2i0000000000000000000000
χ7288-8-8080-800-4-444000000-4040000000000000000000−4i4i000000000000002i−2i2i−2i0000000000000000000000
χ7388-8-80-8080088-8-8000000-8080000000000000000000000000000000000000000000000000000000000000
χ7488-8-80-80800-4-44400000040-400000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000
χ7588-8-80-80800-4-44400000040-4000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000
χ768-88-880000-8-444-4008-8-440000000000-440000000000000000000000000000000000000000000000000000
χ778-88-880000-8-444-400-88-4400000000004-40000000000000000000000000000000000000000000000000000
χ788-88-8-800008-444-48-8004-400000000-44000000000000000000000000000000000000000000000000000000
χ798-88-8-800008-444-4-88004-4000000004-4000000000000000000000000000000000000000000000000000000
χ808-8-880080-808-88-8000000080-8000000000000000000000000000000000000000000000000000000000000
χ818-8-880080-80-44-440000000-40400000000000000000000000000000023−23−232300000000000000000000000000
χ828-8-880080-80-44-440000000-404000000000000000000000000000000−232323−2300000000000000000000000000
χ838-8-8800-8080-44-44000000040-400000000000000004-4000000000000-22-2200000000000000000000000000
χ848-8-8800-8080-44-44000000040-40000000000000000-440000000000002-22-200000000000000000000000000

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