Finite Group Databasebeta

← Group #13148642

Character table — Group #13148642

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222224444446666666612121212121212121212121212121212181818181818181818181818181818181818242424242424363636363636363636363636363636363636363636363636363636
order1222223444466666121212123366666636666666121212121212121222224466666666121212126612121212222444444666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-11-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-11-1-1-11-11-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-111
χ51111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-111
χ61111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-111-11-11-11111-1-1-1-1-1-1111111-1-1
χ71111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-11111-11-1-1-1-11111111111-1-1-1-1-1-1
χ81111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1111111
χ91111-1-1111-1-1111-1-111-1-1111111111-1-1-1-11111111-1-1-1-1111111111111111111-1-111-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ101111-1-1111-1-1111-1-111-1-1111111111-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-11-1-111-1-1111111-1-1-1-1-1-11111
χ111111-1-1111-1-1111-1-111-1-1111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-11-1-111-111111-1-1-1-111-1-111-1-111
χ121111-1-1111-1-1111-1-111-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11-1-111-111-1-111-1-11111-1-111-1-1
χ131111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-1-1-11111111111111111111111-1-1-1-111-1-11-1-1-111-1-1-111-1-1-1-111-1-1-1-111-1-1
χ141111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-11-111-11-1-1-1-111-1-1111111-1-111
χ151111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-111-1-111-1-11111
χ161111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-111111111-1-1-1-111-1-1-1-1
χ17222222222222222222222-1-122-1-12-122-1-1-1-1-122-1-1-1-1220022000000-1-1-1-10000-1-1-1-1-1-10200020200000-1-1000000-1-1-1-100
χ18222222222222222222222-1-122-1-12-122-1-1-1-1-122-1-1-1-12200-2-200000011110000-1-1-1-1-1-10-2000-20-20000011000000111100
χ1922222222222222222222-122-1-122-1-1-1-122-1-1-1-1-12222-1-100002200000000-1-1-1-1-1-1-1-1-1-100220000200-1-1000000-1-10000-1-1
χ2022222222222222222222-122-1-122-1-1-1-122-1-1-1-1-12222-1-10000-2-2000000001111-1-1-1-1-1-100-2-20000-2001100000011000011
χ212222222-2-2-2-222222-2-2-2-22-1-122-1-12-122-1-1-1-1-1-2-21111-2-20022000000-1-1-1-10000-1-1111102000-20-200000-1-1000000111100
χ222222222-2-2-2-222222-2-2-2-22-1-122-1-12-122-1-1-1-1-1-2-21111-2-200-2-200000011110000-1-111110-20002020000011000000-1-1-1-100
χ232222222-2-2-2-222222-2-2-2-2-122-1-122-1-1-1-122-1-1-111-2-2-2-21100002200000000-1-1-1-1-1-1111100-2-2000020011000000110000-1-1
χ242222222-2-2-2-222222-2-2-2-2-122-1-122-1-1-1-122-1-1-111-2-2-2-2110000-2-2000000001111-1-1111100220000-200-1-1000000-1-1000011
χ252222-2-2222-2-2222-2-222-2-22-1-122-1-12-1-2-211-1-1-122-1-111-2-20022000000-1-1-1-1000011-1-1110-200020-20000011000000-1-11100
χ262222-2-2222-2-2222-2-222-2-22-1-122-1-12-1-2-211-1-1-122-1-111-2-200-2-20000001111000011-1-11102000-20200000-1-100000011-1-100
χ272222-2-2222-2-2222-2-222-2-2-122-1-122-1-111-2-2-1-1-1-1-122-2-21100002200000000-1-1-1-111-1-11100-220000-20011000000-1-1000011
χ282222-2-2222-2-2222-2-222-2-2-122-1-122-1-111-2-2-1-1-1-1-122-2-2110000-2-200000000111111-1-111002-20000200-1-1000000110000-1-1
χ292222-2-22-2-222222-2-2-2-2222-1-122-1-12-1-2-211-1-1-1-2-211-1-1220022000000-1-1-1-100001111-1-10-2000-202000001100000011-1-100
χ302222-2-22-2-222222-2-2-2-2222-1-122-1-12-1-2-211-1-1-1-2-211-1-12200-2-2000000111100001111-1-10200020-200000-1-1000000-1-11100
χ312222-2-22-2-222222-2-2-2-222-122-1-122-1-111-2-2-1-1-111-2-222-1-100002200000000-1-1-1-11111-1-1002-20000-200-1-100000011000011
χ322222-2-22-2-222222-2-2-2-222-122-1-122-1-111-2-2-1-1-111-2-222-1-10000-2-20000000011111111-1-100-22000020011000000-1-10000-1-1
χ3322-2-22-222i−2i2i−2i2-2-22-22i−2i2i−2i222-22-2-2-222-22-22-2-22i−2i2i−2i2i−2i2i−2i0000000000000000002-22i−2i2i−2i000000000000000000000000000
χ3422-2-22-222i−2i2i−2i2-2-22-22i−2i2i−2i2-1-1-2211-2-12-2-11-1112i−2i−ii−ii2i−2i0000000000−i3−i3i3i30000-11−ii−ii0000000000000−i3i30000003−33−300
χ3522-2-22-222i−2i2i−2i2-2-22-22i−2i2i−2i2-1-1-2211-2-12-2-11-1112i−2i−ii−ii2i−2i0000000000i3i3−i3−i30000-11−ii−ii0000000000000i3−i3000000−33−3300
χ3622-2-22-222i−2i2i−2i2-2-22-22i−2i2i−2i-1221-1-2-21-1-112-2-111−ii2i−2i2i−2i−ii0000000000000033−3−3-11−ii−ii00000000000−i3i3000000−i3i300003−3
χ3722-2-22-222i−2i2i−2i2-2-22-22i−2i2i−2i-1221-1-2-21-1-112-2-111−ii2i−2i2i−2i−ii00000000000000−3−333-11−ii−ii00000000000i3−i3000000i3−i30000−33
χ3822-2-22-22−2i2i−2i2i2-2-22-2−2i2i−2i2i222-22-2-2-222-22-22-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000002-2−2i2i−2i2i000000000000000000000000000
χ3922-2-22-22−2i2i−2i2i2-2-22-2−2i2i−2i2i2-1-1-2211-2-12-2-11-111−2i2ii−ii−i−2i2i0000000000−i3−i3i3i30000-11i−ii−i0000000000000−i3i3000000−33−3300
χ4022-2-22-22−2i2i−2i2i2-2-22-2−2i2i−2i2i2-1-1-2211-2-12-2-11-111−2i2ii−ii−i−2i2i0000000000i3i3−i3−i30000-11i−ii−i0000000000000i3−i30000003−33−300
χ4122-2-22-22−2i2i−2i2i2-2-22-2−2i2i−2i2i-1221-1-2-21-1-112-2-111i−i−2i2i−2i2ii−i0000000000000033−3−3-11i−ii−i00000000000i3−i3000000i3−i300003−3
χ4222-2-22-22−2i2i−2i2i2-2-22-2−2i2i−2i2i-1221-1-2-21-1-112-2-111i−i−2i2i−2i2ii−i00000000000000−3−333-11i−ii−i00000000000−i3i3000000−i3i30000−33
χ4322-2-2-2222i−2i−2i2i2-2-2-222i−2i−2i2i222-22-2-2-22-22-222-2-22i−2i2i−2i−2i2i−2i2i000000000000000000-222i−2i−2i2i000000000000000000000000000
χ4422-2-2-2222i−2i−2i2i2-2-2-222i−2i−2i2i2-1-1-2211-2-1-221-1-1112i−2i−iii−i−2i2i0000000000−i3−i3i3i300001-1−iii−i0000000000000i3−i30000003−3−3300
χ4522-2-2-2222i−2i−2i2i2-2-2-222i−2i−2i2i2-1-1-2211-2-1-221-1-1112i−2i−iii−i−2i2i0000000000i3i3−i3−i300001-1−iii−i0000000000000−i3i3000000−333−300
χ4622-2-2-2222i−2i−2i2i2-2-2-222i−2i−2i2i-1221-1-2-21-11-1-22-111−ii2i−2i−2i2ii−i0000000000000033−3−31-1−iii−i00000000000i3−i3000000−i3i30000−33
χ4722-2-2-2222i−2i−2i2i2-2-2-222i−2i−2i2i-1221-1-2-21-11-1-22-111−ii2i−2i−2i2ii−i00000000000000−3−3331-1−iii−i00000000000−i3i3000000i3−i300003−3
χ4822-2-2-222−2i2i2i−2i2-2-2-22−2i2i2i−2i222-22-2-2-22-22-222-2-2−2i2i−2i2i2i−2i2i−2i000000000000000000-22−2i2i2i−2i000000000000000000000000000
χ4922-2-2-222−2i2i2i−2i2-2-2-22−2i2i2i−2i2-1-1-2211-2-1-221-1-111−2i2ii−i−ii2i−2i0000000000−i3−i3i3i300001-1i−i−ii0000000000000i3−i3000000−333−300
χ5022-2-2-222−2i2i2i−2i2-2-2-22−2i2i2i−2i2-1-1-2211-2-1-221-1-111−2i2ii−i−ii2i−2i0000000000i3i3−i3−i300001-1i−i−ii0000000000000−i3i30000003−3−3300
χ5122-2-2-222−2i2i2i−2i2-2-2-22−2i2i2i−2i-1221-1-2-21-11-1-22-111i−i−2i2i2i−2i−ii0000000000000033−3−31-1i−i−ii00000000000−i3i3000000i3−i30000−33
χ5222-2-2-222−2i2i2i−2i2-2-2-22−2i2i2i−2i-1221-1-2-21-11-1-22-111i−i−2i2i2i−2i−ii00000000000000−3−3331-1i−i−ii00000000000i3−i3000000−i3i300003−3
χ532-2-220020000-22-200000022-2-2-22-2220000-22-2000000002-22-22-222-2-22-22-22-22-2000000000000000000000000000000000
χ542-2-220020000-22-200000022-2-2-22-2220000-22-2000000002-2-22-2222-2-2-22-22-22-22000000000000000000000000000000000
χ552-2-220020000-22-200000022-2-2-22-2220000-22-200000000-222-2-22-2-2222-22-2-22-22000000000000000000000000000000000
χ562-2-220020000-22-200000022-2-2-22-2220000-22-200000000-22-222-2-2-222-22-222-22-2000000000000000000000000000000000
χ5744444444444444444444-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-2-2-2-2000000000000000000111111000000000000000000000000000
χ584444444-4-4-4-444444-4-4-4-4-2-2-2-2-2-2-2-21-2-2-2-21112222222200000000000000000011-1-1-1-1000000000000000000000000000
χ594444-4-4444-4-4444-4-444-4-4-2-2-2-2-2-2-2-212222111-2-2-2-22222000000000000000000-1-111-1-1000000000000000000000000000
χ604444-4-44-4-444444-4-4-4-444-2-2-2-2-2-2-2-2122221112222-2-2-2-2000000000000000000-1-1-1-111000000000000000000000000000
χ6144-4-44-444i−4i4i−4i4-4-44-44i−4i4i−4i-2-2-22-22221-22-221-1-1−2i2i−2i2i−2i2i−2i2i0000000000000000001-1i−ii−i000000000000000000000000000
χ6244-4-44-44−4i4i−4i4i4-4-44-4−4i4i−4i4i-2-2-22-22221-22-221-1-12i−2i2i−2i2i−2i2i−2i0000000000000000001-1−ii−ii000000000000000000000000000
χ6344-4-4-4444i−4i−4i4i4-4-4-444i−4i−4i4i-2-2-22-222212-22-21-1-1−2i2i−2i2i2i−2i2i−2i000000000000000000-11i−i−ii000000000000000000000000000
χ6444-4-4-444−4i4i4i−4i4-4-4-44−4i4i4i−4i-2-2-22-222212-22-21-1-12i−2i2i−2i−2i2i−2i2i000000000000000000-11−iii−i000000000000000000000000000
χ654-44-40040000-4-4400000044-44-4-44-440000-4-4400000000000000000000000000000000000000000000000000000000000
χ664-44-40040000-4-440000004-224-42-2-4-2000022-2000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ674-44-40040000-4-440000004-224-42-2-4-2000022-20000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ684-44-40040000-4-44000000-24-4-22-442-2000022-2000000000000000000000023−23−2323000000000000000000000000000000000
χ694-44-40040000-4-44000000-24-4-22-442-2000022-20000000000000000000000−232323−23000000000000000000000000000000000
χ704-4-440040000-44-40000004-22-4-4-224-200002-2200000000004-4000000-22-220000000000000000000000000000000000000
χ714-4-440040000-44-40000004-22-4-4-224-200002-220000000000-440000002-22-20000000000000000000000000000000000000
χ724-4-440040000-44-4000000-24-4224-4-2-200002-220000000000004-400000000-22-22000000000000000000000000000000000
χ734-4-440040000-44-4000000-24-4224-4-2-200002-22000000000000-44000000002-22-2000000000000000000000000000000000
χ74666666-36666-3-3-3-3-3-3-3-3-3000000000000000000000000220000-1-1-1-100000000000000200020200-1-10000-1-1-1-100000000
χ75666666-36666-3-3-3-3-3-3-3-3-3000000000000000000000000-2-20000111100000000000000-2000-20-200110000111100000000
χ76666666-3-6-6-6-6-3-3-3-3-33333000000000000000000000000220000-1-1-1-1000000000000002000-20-200-1-10000111100000000
χ77666666-3-6-6-6-6-3-3-3-3-33333000000000000000000000000-2-20000111100000000000000-200020200110000-1-1-1-100000000
χ786666-6-6-366-6-6-3-3-333-3-333000000000000000000000000220000-1-1-1-100000000000000-200020-200110000-1-11100000000
χ796666-6-6-366-6-6-3-3-333-3-333000000000000000000000000-2-200001111000000000000002000-20200-1-1000011-1-100000000
χ806666-6-6-3-6-666-3-3-33333-3-3000000000000000000000000220000-1-1-1-100000000000000-2000-2020011000011-1-100000000
χ816666-6-6-3-6-666-3-3-33333-3-3000000000000000000000000-2-20000111100000000000000200020-200-1-10000-1-11100000000
χ8266-6-66-6-36i−6i6i−6i-333-33−3i3i−3i3i000000000000000000000000000000−i3i3−i3i300000000000000000000000−i3i300003−33−300000000
χ8366-6-66-6-36i−6i6i−6i-333-33−3i3i−3i3i000000000000000000000000000000i3−i3i3−i300000000000000000000000i3−i30000−33−3300000000
χ8466-6-66-6-3−6i6i−6i6i-333-333i−3i3i−3i000000000000000000000000000000−i3i3−i3i300000000000000000000000−i3i30000−33−3300000000
χ8566-6-66-6-3−6i6i−6i6i-333-333i−3i3i−3i000000000000000000000000000000i3−i3i3−i300000000000000000000000i3−i300003−33−300000000
χ8666-6-6-66-36i−6i−6i6i-3333-3−3i3i3i−3i000000000000000000000000000000−i3i3−i3i300000000000000000000000i3−i300003−3−3300000000
χ8766-6-6-66-36i−6i−6i6i-3333-3−3i3i3i−3i000000000000000000000000000000i3−i3i3−i300000000000000000000000−i3i30000−333−300000000
χ8866-6-6-66-3−6i6i6i−6i-3333-33i−3i−3i3i000000000000000000000000000000−i3i3−i3i300000000000000000000000i3−i30000−333−300000000
χ8966-6-6-66-3−6i6i6i−6i-3333-33i−3i−3i3i000000000000000000000000000000i3−i3i3−i300000000000000000000000−i3i300003−3−3300000000
χ908-88-80080000-8-88000000-4-44-444-4420000-2-2200000000000000000000000000000000000000000000000000000000000
χ918-8-880080000-88-8000000-4-4444-44-420000-22-200000000000000000000000000000000000000000000000000000000000
χ9212-1212-1200-6000066-6000000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000
χ9312-1212-1200-6000066-60000000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ9412-12-121200-600006-660000000000000000000000000000004-40000-2-22200000000000000000000000000000000000000000
χ9512-12-121200-600006-66000000000000000000000000000000-44000022-2-200000000000000000000000000000000000000000

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