Finite Group Databasebeta

← Group #13140587

Character table — Group #13140587

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222222444466668812121212121212121212121212122424242424242424363636363636363636363636363636363636727272727272727272
order1222236662466336661236666666666612126666612121222444466661212121212121212444121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111-1-1111111-1-111111-1-111111-1-1-111-1-1-1-1-11-11-11111-1-1111111-1-1-11-1-1-111-1-1
χ6111111111-1-1111111-1-111111-1-111111-1-1-111-1-1-1-1-11-11-1-1-111-1-1-1-1-1-111-1-11-1111-1-111
χ7111111111-1-1111111-1-111111-1-111111-1-1-111-1-1-1-1-1-11-1111-1-1111111-1-111-1-11-1-1-1-111
χ8111111111-1-1111111-1-111111-1-111111-1-1-111-1-1-1-1-1-11-11-1-1-1-111-1-1-1-1-1-11111-11111-1-1
χ922222222222222-12-122-12-1-1-1-1-1-1-1-122-1-12-1-1-1-12-1-1222200-1-1-1-10000-1-1-1-1000000000
χ1022222222222222-12-122-12-1-1-1-1-1-1-1-122-1-12-1-1-1-12-1-1-2-2-2-200111100001111000000000
χ112222222222222-12-1222-1-122222-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000000002200-1-1-1-1
χ122222222222222-12-1222-1-122222-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000-2-2001111
χ13222222222-2-2222-12-1-2-2-12-1-1-111-1-1-12211-2-1-111-2112-22-200-1-1110000-1-111000000000
χ14222222222-2-2222-12-1-2-2-12-1-1-111-1-1-12211-2-1-111-211-22-220011-1-1000011-1-1000000000
χ15222222222-2-222-12-12-2-2-1-1222-2-2-1-1-1-1-1-2-21-1-11111100000000000000000002-200-1-111
χ16222222222-2-222-12-12-2-2-1-1222-2-2-1-1-1-1-1-2-21-1-1111110000000000000000000-220011-1-1
χ17222-2-222222-2-2-222222-2222-2-222222-2-2-2-22-2-222-2-2-2000000000000000000000000000
χ18222-2-222222-2-2-22-12-12-2-12-111-1-1-1-1-1-2-211211-1-1-211000000−i3i3−i3i30000−i3i3−i3i3000000000
χ19222-2-222222-2-2-22-12-12-2-12-111-1-1-1-1-1-2-211211-1-1-211000000i3−i3i3−i30000i3−i3i3−i3000000000
χ20222-2-222222-2-2-2-12-122-2-1-12-2-222-1-1-111-2-2-111-1-1111000000000000000000000003−33−3
χ21222-2-222222-2-2-2-12-122-2-1-12-2-222-1-1-111-2-2-111-1-111100000000000000000000000−33−33
χ22222-2-22222-22-2-22222-22222-2-2-2-2222-2-222-2-2-2-2-2222000000000000000000000000000
χ23222-2-22222-22-2-22-12-1-22-12-11111-1-1-1-2-2-1-1-211112-1-1000000−i3i3i3−i30000−i3i3i3−i3000000000
χ24222-2-22222-22-2-22-12-1-22-12-11111-1-1-1-2-2-1-1-211112-1-1000000i3−i3−i3i30000i3−i3−i3i3000000000
χ25222-2-22222-22-2-2-12-12-22-1-12-2-2-2-2-1-1-1112211111-1-1-1000000000000000000000003−3−33
χ26222-2-22222-22-2-2-12-12-22-1-12-2-2-2-2-1-1-1112211111-1-1-100000000000000000000000−333−3
χ2722-22-22-2-22002-22222002-2-22-200-2-222-20002-200000020-2000022000000-2-2000000000
χ2822-22-22-2-22002-22222002-2-22-200-2-222-20002-2000000-2020000-2-200000022000000000
χ2922-22-22-2-22002-22-12-100-1-21-11−i3i311-12-2−i3i30-11−i3i30−i3i3020-200−i3i3-1-10000i3−i311000000000
χ3022-22-22-2-22002-22-12-100-1-21-11−i3i311-12-2−i3i30-11−i3i30−i3i30-20200i3−i3110000−i3i3-1-1000000000
χ3122-22-22-2-22002-22-12-100-1-21-11i3−i311-12-2i3−i30-11i3−i30i3−i3020-200i3−i3-1-10000−i3i311000000000
χ3222-22-22-2-22002-22-12-100-1-21-11i3−i311-12-2i3−i30-11i3−i30i3−i30-20200−i3i3110000i3−i3-1-1000000000
χ3322-2-222-2-2200-222222002-2-2-2200-2-22-22000-220000020-200022000000-2-200000000000
χ3422-2-222-2-2200-222222002-2-2-2200-2-22-22000-2200000-202000-2-20000002200000000000
χ3522-2-222-2-2200-222-12-100-1-211-1−i3i311-1-22i3−i301-1−i3i30i3−i320-2000-1-1−i3i3000011i3−i3000000000
χ3622-2-222-2-2200-222-12-100-1-211-1−i3i311-1-22i3−i301-1−i3i30i3−i3-20200011i3−i30000-1-1−i3i3000000000
χ3722-2-222-2-2200-222-12-100-1-211-1i3−i311-1-22−i3i301-1i3−i30−i3i320-2000-1-1i3−i3000011−i3i3000000000
χ3822-2-222-2-2200-222-12-100-1-211-1i3−i311-1-22−i3i301-1i3−i30−i3i3-20200011−i3i30000-1-1i3−i3000000000
χ394444444444444-2-2-2-2441-2-2-2-2-2-2111-2-2-2-2-21111-211000000000000000000000000000
χ40444444444-4-444-2-2-2-2-4-41-2-2-2-222111-2-222211-1-12-1-1000000000000000000000000000
χ41444-4-444444-4-4-4-2-2-2-24-41-2-222-2-21112222-2-1-1112-1-1000000000000000000000000000
χ42444-4-44444-44-4-4-2-2-2-2-441-2-2222211122-2-22-1-1-1-1-211000000000000000000000000000
χ4344-44-44-4-44004-4-24-2400-22-44-40022-2-22000-2200000000000000000000000000000000
χ4444-44-44-4-44004-4-2-2-2-200122-22−2i32i3-1-11-22−2i32i301-1i3−i30i3−i3000000000000000000000000000
χ4544-44-44-4-44004-4-2-2-2-200122-222i3−2i3-1-11-222i3−2i301-1−i3i30−i3i3000000000000000000000000000
χ4644-4-444-4-4400-44-24-2400-22-4-440022-22-20002-200000000000000000000000000000000
χ4744-4-444-4-4400-44-2-2-2-2001222-2−2i32i3-1-112-22i3−2i30-11i3−i30−i3i3000000000000000000000000000
χ4844-4-444-4-4400-44-2-2-2-2001222-22i3−2i3-1-112-2−2i32i30-11−i3i30i3−i3000000000000000000000000000
χ494-4000400-4000044-4-400400000000-400000000000000002i−2i00002i2i−2i−2i0000000000000
χ504-4000400-4000044-4-400400000000-40000000000000000−2i2i0000−2i−2i2i2i0000000000000
χ5166666-3-3-3-366-3-30000-3-300000000000000000000000000220000-1-1-1-10000200-1-10000
χ5266666-3-3-3-366-3-30000-3-300000000000000000000000000-2-2000011110000-200110000
χ5366666-3-3-3-3-6-6-3-300003300000000000000000000000000220000-1-1-1-10000-200110000
χ5466666-3-3-3-3-6-6-3-300003300000000000000000000000000-2-2000011110000200-1-10000
χ55666-6-6-3-3-3-36-6330000-3300000000000000000000000000000000−i3i3−i3i30000000−i3i30000
χ56666-6-6-3-3-3-36-6330000-3300000000000000000000000000000000i3−i3i3−i30000000i3−i30000
χ57666-6-6-3-3-3-3-663300003-300000000000000000000000000000000−i3i3−i3i30000000i3−i30000
χ58666-6-6-3-3-3-3-663300003-300000000000000000000000000000000i3−i3i3−i30000000−i3i30000
χ598-8000800-800008-4-8400-4000000004000000000000000000000000000000000000000
χ608-8000800-80000-484-800-4000000004000000000000000000000000000000000000000
χ618-8000800-80000-4-4440020000006-6-2000000000000000000000000000000000000000
χ628-8000800-80000-4-444002000000-66-2000000000000000000000000000000000000000
χ631212-1212-12-666-600-660000000000000000000000000000000000000000000000000000000
χ641212-12-1212-666-6006-60000000000000000000000000000000000000000000000000000000
χ6512-12000-6−6i36i360000000000000000000000000000000000002i−2i00002ζ72ζ11−2ζ7−2ζ110000000000000
χ6612-12000-6−6i36i36000000000000000000000000000000000000−2i2i0000−2ζ7−2ζ112ζ72ζ110000000000000
χ6712-12000-66i3−6i360000000000000000000000000000000000002i−2i00002ζ112ζ7−2ζ11−2ζ70000000000000
χ6812-12000-66i3−6i36000000000000000000000000000000000000−2i2i0000−2ζ11−2ζ72ζ112ζ70000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.