Finite Group Databasebeta

← Group #13141071

Character table — Group #13141071

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222222444466668812121212121212121212121212122424242424242424363636363636363636363636363636363636727272727272727272
order1223446121224612336661236666612121212121212126666121212122444446612121212121212121212488121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-11-1-1-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111
χ5111111111-1-1111111-1-1111-1-11111-1-1111-11-1-1-11-1-111-1-11111111111-1-1-1-1-1-11-1-1-1-111
χ6111111111-1-1111111-1-1111-1-11111-1-1111-11-1-1-11-1-111-1-1-1-111-1-1-1-111-1-1-1-111-11111-1-1
χ7111111111-1-1111111-1-1111-1-11111-1-1111-11-1-1-11-1-1-1-11111-1-11111-1-111111-1-111-1-1-1-1
χ8111111111-1-1111111-1-1111-1-11111-1-1111-11-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-11111
χ922222222222222-12-122-12-1-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1222200-1-10000-1-1-1-1-1-1000000000
χ1022222222222222-12-122-12-1-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-2-2-2-200110000111111000000000
χ112222222222222-12-1222-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1000000000000000000202-1-100-1-1
χ122222222222222-12-1222-1-1222-1-12222-1-1-1-1-1-1-1-1-1-1-1000000000000000000-20-2110011
χ13222222222-2-2222-12-1-2-2-12-111-12-1-111-1-12-2-111-2-11122-2-200-1-10000-1-11111000000000
χ14222222222-2-2222-12-1-2-2-12-111-12-1-111-1-12-2-111-2-111-2-2220011000011-1-1-1-1000000000
χ15222222222-2-222-12-12-2-2-1-12-2-2-1-122-2-2-1-1-11-1111-11100000000000000000020-2-1-10011
χ16222222222-2-222-12-12-2-2-1-12-2-2-1-122-2-2-1-1-11-1111-111000000000000000000-2021100-1-1
χ172222-2-22-2-2002-2222200222002-2-2-200-2-2-202000-200002-2000000000022-2-2000000000
χ182222-2-22-2-2002-2222200222002-2-2-200-2-2-202000-20000-220000000000-2-222000000000
χ192222-2-22-2-2002-22-12-100-12-1−i3i3-1-211−i3i311-20-1−i3i301−i3i3002-200−i3i30000−i3i3-1-111000000000
χ202222-2-22-2-2002-22-12-100-12-1−i3i3-1-211−i3i311-20-1−i3i301−i3i300-2200i3−i30000i3−i311-1-1000000000
χ212222-2-22-2-2002-22-12-100-12-1i3−i3-1-211i3−i311-20-1i3−i301i3−i3002-200i3−i30000i3−i3-1-111000000000
χ222222-2-22-2-2002-22-12-100-12-1i3−i3-1-211i3−i311-20-1i3−i301i3−i300-2200−i3i30000−i3i311-1-1000000000
χ2322-222-222200-2-22222002-2-200222-20022-20-2000-2002-20000220000-2-20000000000000
χ2422-222-222200-2-22222002-2-200222-20022-20-2000-200-220000-2-20000220000000000000
χ2522-222-222200-2-22-12-100-1-21−i3i3-12-11i3−i3-1-1-201−i3i301i3−i32-20000-1-1000011−i3i3−i3i3000000000
χ2622-222-222200-2-22-12-100-1-21−i3i3-12-11i3−i3-1-1-201−i3i301i3−i3-220000110000-1-1i3−i3i3−i3000000000
χ2722-222-222200-2-22-12-100-1-21i3−i3-12-11−i3i3-1-1-201i3−i301−i3i32-20000-1-1000011i3−i3i3−i3000000000
χ2822-222-222200-2-22-12-100-1-21i3−i3-12-11−i3i3-1-1-201i3−i301−i3i3-220000110000-1-1−i3i3−i3i3000000000
χ2922-22-222-2-22-2-2222222-22-2-2222-2-22-2-2-2-222-222-22-2-2000000000000000000000000000
χ3022-22-222-2-22-2-222-12-12-2-1-21-1-1-1-21-11111221-1-1-2-111000000−i3i30000i3−i3−i3i3i3−i3000000000
χ3122-22-222-2-22-2-222-12-12-2-1-21-1-1-1-21-11111221-1-1-2-111000000i3−i30000−i3i3i3−i3−i3i3000000000
χ3222-22-222-2-22-2-22-12-122-2-11-222-11-22-2-211-1-11-1-11-111000000000000000000000−i3i300−i3i3
χ3322-22-222-2-22-2-22-12-122-2-11-222-11-22-2-211-1-11-1-11-111000000000000000000000i3−i300i3−i3
χ3422-22-222-2-2-22-222222-222-2-2-2-22-2-2222-2-22-2-2-2-22222000000000000000000000000000
χ3522-22-222-2-2-22-222-12-1-22-1-2111-1-21-1-1-1112-21112-1-1-1000000−i3i30000i3−i3i3−i3−i3i3000000000
χ3622-22-222-2-2-22-222-12-1-22-1-2111-1-21-1-1-1112-21112-1-1-1000000i3−i30000−i3i3−i3i3i3−i3000000000
χ3722-22-222-2-2-22-22-12-12-22-11-2-2-2-11-222211-11111-1-1-1-1000000000000000000000−i3i300i3−i3
χ3822-22-222-2-2-22-22-12-12-22-11-2-2-2-11-222211-11111-1-1-1-1000000000000000000000i3−i300−i3i3
χ394444444444444-2-2-2-2441-2-2-2-21-2-2-2-2-211-2-2111-2111000000000000000000000000000
χ40444444444-4-444-2-2-2-2-4-41-2-2221-2-2-22211-221-1-121-1-1000000000000000000000000000
χ414444-4-44-4-4004-4-24-2400-2-2400-22-4-4002220-2000200000000000000000000000000000
χ424444-4-44-4-4004-4-2-2-2-2001-2-2−2i32i31222−2i32i3-1-1201i3−i30-1i3−i3000000000000000000000000000
χ434444-4-44-4-4004-4-2-2-2-2001-2-22i3−2i312222i3−2i3-1-1201−i3i30-1−i3i3000000000000000000000000000
χ4444-444-444400-4-4-24-2400-22-400-2-24-400-2-2202000200000000000000000000000000000
χ4544-444-444400-4-4-2-2-2-200122−2i32i31-2-222i3−2i31120-1i3−i30-1−i3i3000000000000000000000000000
χ4644-444-444400-4-4-2-2-2-2001222i3−2i31-2-22−2i32i31120-1−i3i30-1i3−i3000000000000000000000000000
χ4744-44-444-4-44-4-44-2-2-2-24-4122-2-2122-222-1-1-2-2-11121-1-1000000000000000000000000000
χ4844-44-444-4-4-44-44-2-2-2-2-4412222122-2-2-2-1-1-22-1-1-1-2111000000000000000000000000000
χ494-40400-400000044-4-40040000-4000000000000000000002-20022-2-2000000000000000
χ504-40400-400000044-4-40040000-400000000000000000000-2200-2-222000000000000000
χ51666-366-3-3-366-3-30000-3-3000000000000000000000000002200-1-1-1-100000002000-1-100
χ52666-366-3-3-366-3-30000-3-300000000000000000000000000-2-20011110000000-20001100
χ53666-366-3-3-3-6-6-3-3000033000000000000000000000000002200-1-1-1-10000000-20001100
χ54666-366-3-3-3-6-6-3-300003300000000000000000000000000-2-200111100000002000-1-100
χ5566-6-3-66-3336-63-30000-330000000000000000000000000000003−33−3000000000003−300
χ5666-6-3-66-3336-63-30000-33000000000000000000000000000000−33−3300000000000−3300
χ5766-6-3-66-333-663-300003-30000000000000000000000000000003−33−300000000000−3300
χ5866-6-3-66-333-663-300003-3000000000000000000000000000000−33−33000000000003−300
χ598-80800-80000008-4-8400-4000040000000000000000000000000000000000000000000
χ608-80800-8000000-484-800-4000040000000000000000000000000000000000000000000
χ618-80800-8000000-4-4440020000-2000006i−6i000000000000000000000000000000000000
χ628-80800-8000000-4-4440020000-200000−6i6i000000000000000000000000000000000000
χ63121212-6-12-12-66600-660000000000000000000000000000000000000000000000000000000
χ641212-12-612-12-6-6-600660000000000000000000000000000000000000000000000000000000
χ6512-120-600663−630000000000000000000000000000000000002-200−1+3−1−31−31+3000000000000000
χ6612-120-600663−63000000000000000000000000000000000000-22001−31+3−1+3−1−3000000000000000
χ6712-120-6006−63630000000000000000000000000000000000002-200−1−3−1+31+31−3000000000000000
χ6812-120-6006−6363000000000000000000000000000000000000-22001+31−3−1−3−1+3000000000000000

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