Finite Group Databasebeta

← Group #13167419

Character table — Group #13167419

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1122222224444444444888888888888888888889918181818181818363636363636363636363636363636363636363636367272727272727272
order1223446121233666661212123366666661212121212121212121212222446612122222444468888121212121212121212666624242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-11-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i-1ii−i−i1iiii−i−i−i−i11-1-1ii−i−i
χ61111-1-11-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iii-1−i−iii1−i−i−i−iiiii11-1-1−i−iii
χ71111-1-11-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111ii−i−i-1−i−iii1iiii−i−i−i−i-1-111−i−iii
χ81111-1-11-1-11111111-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111−i−iii-1ii−i−i1−i−i−i−iiiii-1-111ii−i−i
χ911-111-111111-1-1-111-1-1-111-1-1-1-1-11111-11111-1-1-1-1-1-111-1-1-1-1-11-11-1i−ii−i1i−ii−i1ii−i−iii−i−i1-11-1i−ii−i
χ1011-111-111111-1-1-111-1-1-111-1-1-1-1-11111-11111-1-1-1-1-1-111-1-1-1-1-11-11-1−ii−ii1−ii−ii1−i−iii−i−iii1-11-1−ii−ii
χ1111-111-111111-1-1-111-1-1-111-1-1-1-1-11111-11111-1-1-1-1-1-111-1-1-1-1-1-11-11i−ii−i1−ii−ii1ii−i−iii−i−i-11-11−ii−ii
χ1211-111-111111-1-1-111-1-1-111-1-1-1-1-11111-11111-1-1-1-1-1-111-1-1-1-1-1-11-11−ii−ii1i−ii−i1−i−iii−i−iii-11-11i−ii−i
χ1311-11-111-1-111-1-1-11111111-1-1-1-1-111-1-11-1-1-1-1111111-11-111-1-11-1-111-1-11-11-1-11111-1-1-1-1111-1-111-1-11
χ1411-11-111-1-111-1-1-11111111-1-1-1-1-111-1-11-1-1-1-1111111-11-111-1-11-1-11-111-1-1-111-11-1-11111-1-11-1-11-111-1
χ1511-11-111-1-111-1-1-11111111-1-1-1-1-111-1-11-1-1-1-1111111-11-111-1-1-111-11-1-11-1-111-1111-1-1-1-111-111-1-111-1
χ1611-11-111-1-111-1-1-11111111-1-1-1-1-111-1-11-1-1-1-1111111-11-111-1-1-111-1-111-1-11-1-111-1-11111-1-1-111-11-1-11
χ17222222222222222222222222222222222222222-2-2-2-2-2-2-2-2-200000000-20000-20000000000000000
χ182222-2-22-2-22222222-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2222-2-222-2-20000000020000-20000000000000000
χ19222-122-1-1-122-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222-1-1-1-100002222-10000-1-1-1-1-1-1-1-1-100000000
χ20222-122-1-1-122-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222-1-1-1-10000-2-2-2-2-10000-11111111100000000
χ21222-122-1-1-122-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-21111000000001000013−33−33−33−300000000
χ22222-122-1-1-122-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2111100000000100001−33−33−33−3300000000
χ23222-1-2-2-11122-122221-2-2-1-12-1-1-1-1-1-1-2-2-211111111222-2-2-1-11100000000-100001−i3i3−i3i3i3−i3i3−i300000000
χ24222-1-2-2-11122-122221-2-2-1-12-1-1-1-1-1-1-2-2-211111111222-2-2-1-11100000000-100001i3−i3i3−i3−i3i3−i3i300000000
χ25222-1-2-2-11122-122221-2-2-1-12-1-1-1-1-1-1-2-2-211111111-2-2-22211-1-100002i2i−2i−2i10000-1−i−i−i−iiiii00000000
χ26222-1-2-2-11122-122221-2-2-1-12-1-1-1-1-1-1-2-2-211111111-2-2-22211-1-10000−2i−2i2i2i10000-1iiii−i−i−i−i00000000
χ2722-222-222222-2-2-222-2-2-222-2-2-2-2-22222-22222-2-2-2-222-2-22222200000000-20000-20000000000000000
χ2822-22-222-2-222-2-2-22222222-2-2-2-2-222-2-22-2-2-2-22222-2-22-22-2-2220000000020000-20000000000000000
χ2922-2-12-2-1-1-1221-2-2221-2-2-1-1-21111-1-122-2-1-1-1-1111122-2-22-1-1-1-100000000100001−i3i3i3−i3−i3i3i3−i300000000
χ3022-2-12-2-1-1-1221-2-2221-2-2-1-1-21111-1-122-2-1-1-1-1111122-2-22-1-1-1-100000000100001i3−i3−i3i3i3−i3−i3i300000000
χ3122-2-12-2-1-1-1221-2-2221-2-2-1-1-21111-1-122-2-1-1-1-11111-2-222-2111100002i−2i2i−2i-10000-1−i−iii−i−iii00000000
χ3222-2-12-2-1-1-1221-2-2221-2-2-1-1-21111-1-122-2-1-1-1-11111-2-222-211110000−2i2i−2i2i-10000-1ii−i−iii−i−i00000000
χ3322-2-1-22-111221-2-222-122-1-1-21111-1-1-2-221111-1-1-1-122-22-2-1-11100002-2-2210000-1-1-11111-1-100000000
χ3422-2-1-22-111221-2-222-122-1-1-21111-1-1-2-221111-1-1-1-122-22-2-1-1110000-222-210000-111-1-1-1-11100000000
χ3522-2-1-22-111221-2-222-122-1-1-21111-1-1-2-221111-1-1-1-1-2-22-2211-1-100000000-1000013−3−33−333−300000000
χ3622-2-1-22-111221-2-222-122-1-1-21111-1-1-2-221111-1-1-1-1-2-22-2211-1-100000000-100001−333−33−3−3300000000
χ374444444441-24-2-21-24111-2111-2-21-21-2-211-2-211-2-200000000000000000022220000000000000-1-1-1-1
χ384444444441-24-2-21-24111-2111-2-21-21-2-211-2-211-2-2000000000000000000-2-2-2-200000000000001111
χ39444444444-21411-214-2-2-21-2-2-211-21-211-2-211-2-2110000000002222000000000000000000-1-1-1-10000
χ40444444444-21411-214-2-2-21-2-2-211-21-211-2-211-2-211000000000-2-2-2-200000000000000000011110000
χ414444-4-44-4-41-24-2-21-2-4-1-11-2111-2-21-2-122-1-122-1-1220000000000000000002i2i−2i−2i0000000000000−i−iii
χ424444-4-44-4-41-24-2-21-2-4-1-11-2111-2-21-2-122-1-122-1-122000000000000000000−2i−2i2i2i0000000000000ii−i−i
χ434444-4-44-4-4-21411-21-422-21-2-2-211-212-1-122-1-122-1-100000000022-2-2000000000000000000-1-1110000
χ444444-4-44-4-4-21411-21-422-21-2-2-211-212-1-122-1-122-1-1000000000-2-22200000000000000000011-1-10000
χ4544-444-44441-2-4221-2-4-1-11-2-1-1-1221-21-2211-2-2-1-1220000000000000000002i−2i2i−2i0000000000000−ii−ii
χ4644-444-44441-2-4221-2-4-1-11-2-1-1-1221-21-2211-2-2-1-122000000000000000000−2i2i−2i2i0000000000000i−ii−i
χ4744-444-4444-21-4-1-1-21-422-21222-1-1-21-21-1-2-21122-1-10000000002-22-2000000000000000000-11-110000
χ4844-444-4444-21-4-1-1-21-422-21222-1-1-21-21-1-2-21122-1-1000000000-22-220000000000000000001-11-10000
χ4944-44-444-4-41-2-4221-24111-2-1-1-1221-2-12-2-1-12211-2-20000000000000000002-2-220000000000000-111-1
χ5044-44-444-4-41-2-4221-24111-2-1-1-1221-2-12-2-1-12211-2-2000000000000000000-222-200000000000001-1-11
χ5144-44-444-4-4-21-4-1-1-214-2-2-21222-1-1-212-1122-1-1-2-2110000000002-2-22000000000000000000-111-10000
χ5244-44-444-4-4-21-4-1-1-214-2-2-21222-1-1-212-1122-1-1-2-211000000000-222-20000000000000000001-1-110000
χ534-40400-40044000-4-40004400000-4-4000000000004-40004-400000000000000000000000000000000
χ544-40400-40044000-4-40004400000-4-400000000000-44000-4400000000000000000000000000000000
χ554-40-200223−2344000-4-4000-2-2000002200023−2323−2300004-4000-2223−23000000000000000000000000000000
χ564-40-200223−2344000-4-4000-2-2000002200023−2323−230000-440002-2−2323000000000000000000000000000000
χ574-40-2002−232344000-4-4000-2-20000022000−2323−232300004-4000-22−2323000000000000000000000000000000
χ584-40-2002−232344000-4-4000-2-20000022000−2323−23230000-440002-223−23000000000000000000000000000000
χ59888-488-4-4-42-4-4-4-42-4-422-122-1-122-122-4-4-1-122-1-122000000000000000000000000000000000000000
χ60888-488-4-4-4-42-422-42-4-4-42-1-422-1-12-1-42222-1-122-1-1000000000000000000000000000000000000000
χ61888-4-8-8-4442-4-4-4-42-44-2-2-122-1-122-12-24411-2-211-2-2000000000000000000000000000000000000000
χ62888-4-8-8-444-42-422-424442-1-422-1-12-14-2-2-2-211-2-211000000000000000000000000000000000000000
χ6388-8-48-8-4-4-42-44442-44-2-2-12-211-2-2-122-44-1-12211-2-2000000000000000000000000000000000000000
χ6488-8-48-8-4-4-4-424-2-2-424442-14-2-2112-1-42-222-1-1-2-211000000000000000000000000000000000000000
χ6588-8-4-88-4442-44442-4-422-12-211-2-2-12-24-411-2-2-1-122000000000000000000000000000000000000000
χ6688-8-4-88-444-424-2-2-42-4-4-42-14-2-2112-14-22-2-21122-1-1000000000000000000000000000000000000000
χ678-80800-8002-4000-2406i−6i2-400000-2400000006i−6i00000000000000000000000000000000000000000
χ688-80800-8002-4000-240−6i6i2-400000-240000000−6i6i00000000000000000000000000000000000000000
χ698-80800-800-4206-64-2000-420006-64-200000000000000000000000000000000000000000000000000
χ708-80800-800-420-664-2000-42000-664-200000000000000000000000000000000000000000000000000
χ718-80-400443−432-4000-2406i−6i-120−3i33i3001-20003−3−2323−3i3i00000000000000000000000000000000000000000
χ728-80-400443−432-4000-240−6i6i-1203i3−3i3001-20003−3−23233i−3i00000000000000000000000000000000000000000
χ738-80-400443−43-4206-64-20002-1000-33-21000−23233−30033−33000000000000000000000000000000000000000
χ748-80-400443−43-420-664-20002-10003-3-21000−23233−300−3333000000000000000000000000000000000000000
χ758-80-4004−43432-4000-2406i−6i-1203i3−3i3001-2000−3323−23−3i3i00000000000000000000000000000000000000000
χ768-80-4004−43432-4000-240−6i6i-120−3i33i3001-2000−3323−233i−3i00000000000000000000000000000000000000000
χ778-80-4004−4343-4206-64-20002-1000-33-2100023−23−3300−3333000000000000000000000000000000000000000
χ788-80-4004−4343-420-664-20002-10003-3-2100023−23−330033−33000000000000000000000000000000000000000

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