Finite Group Databasebeta

← Group #13167081

Character table — Group #13167081

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122224444444444444444444888888888888888818182424242424242424242424242424242424243636363636727272727272108108108108
order12223666333346666666666661212366612121212121212121212121244441212121212121212121212121212121241212121244121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-111-1-11-111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-111-1-1-11-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1111111-111-1-11-111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1111111-111-1-1-11-1-11111-1-1
χ92222222222222222222222222222222222222222222-2-2000000000000000000-2-2-2-2-20000000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000002-2-2220000000000
χ112222-1-1-1-122-1-12222-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-12-1-1-1-10000000000
χ122222-1-1-1-122-1-12222-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-122-2-21111-2-21111-2-211112-1-1-1-10000000000
χ132222-1-1-1-122-1-12222-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-211110000000000
χ142222-1-1-1-122-1-12222-1-1-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-211110000000000
χ152222-1-1-1-122-1-1-2222-1-1-1-12-1-12211-1-1-1-1-2-21111-2-21111222-2-1-11122-1-1-1-1-2-21111-2-1-1110000000000
χ162222-1-1-1-122-1-1-2222-1-1-1-12-1-12211-1-1-1-1-2-21111-2-2111122-2211-1-1-2-2111122-1-1-1-1-2-1-1110000000000
χ172222-1-1-1-122-1-1-2222-1-1-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-200−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3211-1-10000000000
χ182222-1-1-1-122-1-1-2222-1-1-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-200i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3211-1-10000000000
χ1922-2-222-2-22222022-222-2-2-2-2-2-2-20022-2-20000000000002-200000000000000000002-200000000002-2
χ2022-2-222-2-22222022-222-2-2-2-2-2-2-20022-2-20000000000002-200000000000000000002-20000000000-22
χ2122-2-222-2-22222022-222-2-2-2-2-2-2-20022-2-2000000000000-220000000000000000000-22000000002-200
χ2222-2-222-2-22222022-222-2-2-2-2-2-2-20022-2-2000000000000-220000000000000000000-2200000000-2200
χ23444444441-21141-211111111-2-244-2-2-2-2111111-2-2-2-2-2-200222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ24444444441-21141-211111111-2-244-2-2-2-2111111-2-2-2-2-2-200-2-2-2-2-2-2111111111111000000000000000
χ25444444441-211-41-211111111-2-2-4-4-2-2-2-2-1-1-1-1-1-1222222002-222-2-2-1-1-1-1-1-1111111000000000000000
χ26444444441-211-41-211111111-2-2-4-4-2-2-2-2-1-1-1-1-1-122222200-22-2-222111111-1-1-1-1-1-1000000000000000
χ2744444444-21-2-24-21-2-2-2-2-2-2-2-211441111-2-2-2-2-2-2111111000000000000000000000000022-1-1-1-10000
χ2844444444-21-2-24-21-2-2-2-2-2-2-2-211441111-2-2-2-2-2-21111110000000000000000000000000-2-211110000
χ2944444444-21-2-2-4-21-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-100000000000000000000000002-2-1-1110000
χ3044444444-21-2-2-4-21-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-10000000000000000000000000-2211-1-10000
χ314444-2-2-2-21-2−1−3i32−1+3i3241-21−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-211110022−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000
χ324444-2-2-2-21-2−1−3i32−1+3i3241-21−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111100-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ334444-2-2-2-21-2−1−3i32−1+3i32-41-21−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-1002-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ344444-2-2-2-21-2−1−3i32−1+3i32-41-21−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+3i321+3i321−3i321−3i3222-1-1-1-100-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000
χ354444-2-2-2-21-2−1+3i32−1−3i3241-21−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-211110022−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000
χ364444-2-2-2-21-2−1+3i32−1−3i3241-21−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111100-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ374444-2-2-2-21-2−1+3i32−1−3i32-41-21−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321−3i321+3i321+3i3222-1-1-1-1002-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ384444-2-2-2-21-2−1+3i32−1−3i32-41-21−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321−3i321+3i321+3i3222-1-1-1-100-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000
χ3944-4-4-2-22244-2-2044-4-2-222-422-4-400-2-2220000000000004-40000000000000000000-22000000000000
χ4044-4-4-2-22244-2-2044-4-2-222-422-4-400-2-222000000000000-4400000000000000000002-2000000000000
χ414-44-44-44-444440-4-44-4-444-4-4-44-4004-44-400000000000000000000000000000000000000000000000
χ424-44-44-44-4-21-2-202-1-222-2-22221-1001-11-10000003i−3i3i3i−3i−3i000000000000000000000000000−i3i33−30000
χ434-44-44-44-4-21-2-202-1-222-2-22221-1001-11-10000003i−3i3i3i−3i−3i000000000000000000000000000i3−i3−330000
χ444-44-44-44-4-21-2-202-1-222-2-22221-1001-11-1000000−3i3i−3i−3i3i3i000000000000000000000000000−i3i3−330000
χ454-44-44-44-4-21-2-202-1-222-2-22221-1001-11-1000000−3i3i−3i−3i3i3i000000000000000000000000000i3−i33−30000
χ464-44-4-22-2244-2-20-4-4422-2-2-4224-400-22-2200000000000000000000000000000000000−2i32i30000000000
χ474-44-4-22-2244-2-20-4-4422-2-2-4224-400-22-22000000000000000000000000000000000002i3−2i30000000000
χ484-4-444-4-441-2110-12-1-1-1-1-11112-200-222-23-33-33-300000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000
χ494-4-444-4-441-2110-12-1-1-1-1-11112-200-222-23-33-33-300000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000
χ504-4-444-4-441-2110-12-1-1-1-1-11112-200-222-2-33-33-3300000000000000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3000000000000000
χ514-4-444-4-441-2110-12-1-1-1-1-11112-200-222-2-33-33-3300000000000000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3000000000000000
χ524-4-444-4-4444440-4-4-4-4-4-4-4444-44004-4-4400000000000000000000000000000000000000000000000
χ534-4-44-222-21-2−1−3i32−1+3i320-12-11+3i321−3i321+3i321−3i321−1−3i32−1+3i322-2−2i32i31-1-113-3−3−i323+i32−3+i323−i3200−i3i3−i3i300000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i32000000000000000
χ544-4-44-222-21-2−1−3i32−1+3i320-12-11+3i321−3i321+3i321−3i321−1−3i32−1+3i322-2−2i32i31-1-113-3−3−i323+i32−3+i323−i3200−i3i3−i3i300000000i3−i33−i32−3+i32−3−i323+i32i3−i33−i32−3+i32−3−i323+i32000000000000000
χ554-4-44-222-21-2−1−3i32−1+3i320-12-11+3i321−3i321+3i321−3i321−1−3i32−1+3i322-22i3−2i31-1-11-333+i32−3−i323−i32−3+i3200i3−i3i3−i300000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i32000000000000000
χ564-4-44-222-21-2−1−3i32−1+3i320-12-11+3i321−3i321+3i321−3i321−1−3i32−1+3i322-22i3−2i31-1-11-333+i32−3−i323−i32−3+i3200i3−i3i3−i300000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i32000000000000000
χ574-4-44-222-21-2−1+3i32−1−3i320-12-11−3i321+3i321−3i321+3i321−1+3i32−1−3i322-2−2i32i31-1-11-333−i32−3+i323+i32−3−i3200−i3i3−i3i300000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i32000000000000000
χ584-4-44-222-21-2−1+3i32−1−3i320-12-11−3i321+3i321−3i321+3i321−1+3i32−1−3i322-2−2i32i31-1-11-333−i32−3+i323+i32−3−i3200−i3i3−i3i300000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i32000000000000000
χ594-4-44-222-21-2−1+3i32−1−3i320-12-11−3i321+3i321−3i321+3i321−1+3i32−1−3i322-22i3−2i31-1-113-3−3+i323−i32−3−i323+i3200i3−i3i3−i300000000−i3i33+i32−3−i32−3+i323−i32−i3i33+i32−3−i32−3+i323−i32000000000000000
χ604-4-44-222-21-2−1+3i32−1−3i320-12-11−3i321+3i321−3i321+3i321−1+3i32−1−3i322-22i3−2i31-1-113-3−3+i323−i32−3−i323+i3200i3−i3i3−i300000000i3−i3−3−i323+i323−i32−3+i32i3−i3−3−i323+i323−i32−3+i32000000000000000
χ614-4-44-222-244-2-20-4-4-422224-2-2-44−2i32i3-222-200−2i32i32i3−2i3002i3−2i32i3−2i300000000000000000000000000000000000
χ624-4-44-222-244-2-20-4-4-422224-2-2-442i3−2i3-222-2002i3−2i3−2i32i300−2i32i3−2i32i300000000000000000000000000000000000
χ638888-4-4-4-4-42228-42-42222-42222-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000
χ648888-4-4-4-4-4222-8-42-42222-4222244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000
χ6588-8-888-8-82-42202-4-222-2-2-2-2-24400-4-44400000000000000000000000000000000000000000000000
χ6688-8-888-8-8-42-4-40-424-4-444444-2-20022-2-200000000000000000000000000000000000000000000000
χ6788-8-8-4-4442-4−1−3i3−1+3i302-4-2−1−3i3−1+3i31+3i31−3i3-21+3i31−3i3440022-2-200000000000000000000000000000000000000000000000
χ6888-8-8-4-4442-4−1+3i3−1−3i302-4-2−1+3i3−1−3i31−3i31+3i3-21−3i31+3i3440022-2-200000000000000000000000000000000000000000000000
χ6988-8-8-4-444-42220-42422-2-24-2-2-2-200-1-1110000000033−33−333300000000000000000000000000000000000
χ7088-8-8-4-444-42220-42422-2-24-2-2-2-200-1-11100000000−333333−3300000000000000000000000000000000000
χ718-88-88-88-82-4220-242-2-222-2-2-2-4400-44-4400000000000000000000000000000000000000000000000
χ728-88-8-44-442-4−1−3i3−1+3i30-2421+3i31−3i3−1−3i3−1+3i3-21+3i31−3i3-44002-22-200000000000000000000000000000000000000000000000
χ738-88-8-44-442-4−1+3i3−1−3i30-2421−3i31+3i3−1+3i3−1−3i3-21−3i31+3i3-44002-22-200000000000000000000000000000000000000000000000
χ748-88-8-44-44-422204-2-4-2-2224-2-22-200-11-110000006i−6i−3i−3i3i3i00000000000000000000000000000000000
χ758-88-8-44-44-422204-2-4-2-2224-2-22-200-11-11000000−6i6i3i3i−3i−3i00000000000000000000000000000000000
χ768-8-888-8-88-42-4-404-244444-4-4-4-22002-2-2200000000000000000000000000000000000000000000000
χ778-8-88-444-4-422204-24-2-2-2-2-422-22−4i34i3-111-1002i3−2i3−2i32i300i3−i3i3−i300000000000000000000000000000000000
χ788-8-88-444-4-422204-24-2-2-2-2-422-224i3−4i3-111-100−2i32i32i3−2i300−i3i3−i3i300000000000000000000000000000000000

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