Finite Group Databasebeta

← Group #11920705

Character table — Group #11920705

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222666666668888888812121212121212121212121212121212161616161616161624242424242424242424242424243636363636367272
order12224444366612121212224488883666121212126688881212242424242424242436661212121224661212242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ311111111111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111-1-1-1-11111-1-1-1-1-1-111ii−i−i1111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iii−i−ii−ii−i
χ61111-1-1-1-11111-1-1-1-1-1-111ii−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−iiii−i−ii
χ71111-1-1-1-11111-1-1-1-1-1-111−i−iii1111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−iii−ii−ii
χ81111-1-1-1-11111-1-1-1-1-1-111−i−iii1111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111−i−i−i−iiiiiii−i−i−iii−i
χ9222222222222222222222222-1-1-1-1-1-1-1-12200002200000000-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-100002200
χ1022222222222222222222-2-2-2-2-1-1-1-1-1-1-1-12200002200000000-1-1-1-1-1-1-1-1000000111111110000-2-200
χ1122222222-1-1-1-1-1-1-1-12222000022222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000000000
χ1222222222-1-1-1-1-1-1-1-12222000022222222-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000000000
χ132222-2-2-2-22222-2-2-2-2-2-2222i2i−2i−2i-1-1-1-11111-2-200002200000000-1-1-1-11111000000−i−i−i−iiiii00002i−2i00
χ142222-2-2-2-22222-2-2-2-2-2-222−2i−2i2i2i-1-1-1-11111-2-200002200000000-1-1-1-11111000000iiii−i−i−i−i0000−2i2i00
χ152222-2-2-2-2-1-1-1-11111-2-22200002222-2-2-2-21122-2-2-1-1-1-1-1-11111-1-1-1-111112-2-1-1110000000000000000
χ162222-2-2-2-2-1-1-1-11111-2-22200002222-2-2-2-211-2-222-1-11111-1-1-1-1-1-1-1-11111-2211-1-10000000000000000
χ1722-2-22i−2i2i−2i22-2-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-11-11i−ii−i00−i2i22−200−i2−i2i2i222−2−2-11-11ii−i−i000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131−i−1+i1+i−1−i0000
χ1822-2-22i−2i2i−2i22-2-22i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-11-11i−ii−i00i2−i2−2200i2i2−i2−i2−2−222-11-11ii−i−i000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−1+i1−i−1−i1+i0000
χ1922-2-22i−2i2i−2i22-2-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-11-11i−ii−i00−i2i22−200−i2−i2i2i222−2−2-11-11ii−i−i000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−1+i1−i−1−i1+i0000
χ2022-2-22i−2i2i−2i22-2-22i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-11-11i−ii−i00i2−i2−2200i2i2−i2−i2−2−222-11-11ii−i−i000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131−i−1+i1+i−1−i0000
χ2122-2-2−2i2i−2i2i22-2-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-11-11−ii−ii00−i2i2−2200−i2−i2i2i2−2−222-11-11−i−iii000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−1−i1+i−1+i1−i0000
χ2222-2-2−2i2i−2i2i22-2-2−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-11-11−ii−ii00i2−i22−200i2i2−i2−i222−2−2-11-11−i−iii000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231+i−1−i1−i−1+i0000
χ2322-2-2−2i2i−2i2i22-2-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-11-11−ii−ii00−i2i2−2200−i2−i2i2i2−2−222-11-11−i−iii000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231+i−1−i1−i−1+i0000
χ2422-2-2−2i2i−2i2i22-2-2−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-11-11−ii−ii00i2−i22−200i2i2−i2−i222−2−2-11-11−i−iii000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−1−i1+i−1+i1−i0000
χ252-2-2222-2-22-2-222-22-22-2-2200002-2-22-2-2222-20000-22000000002-2-222-22-20000000000000000000000
χ262-2-2222-2-22-2-222-22-22-2-220000-111-111-1-12-20000-2200000000-111-1-11-11000000−i3i3−i3i3−i3i3−i3i300000000
χ272-2-2222-2-22-2-222-22-22-2-220000-111-111-1-12-20000-2200000000-111-1-11-11000000i3−i3i3−i3i3−i3i3−i300000000
χ282-2-2222-2-2-111-1-11-112-2-2200002-2-22-2-222-1100001-1−i3i3−i3i3−i3i3−i3i3-111-1-11-1100−i3i3−i3i30000000000000000
χ292-2-2222-2-2-111-1-11-112-2-2200002-2-22-2-222-1100001-1i3−i3i3−i3i3−i3i3−i3-111-1-11-1100i3−i3i3−i30000000000000000
χ302-2-22-2-2222-2-22-22-22-22-2200002-2-2222-2-2-220000-22000000002-2-22-22-220000000000000000000000
χ312-2-22-2-2222-2-22-22-22-22-220000-111-1-1-111-220000-2200000000-111-11-11-10000003−33−3−33−3300000000
χ322-2-22-2-2222-2-22-22-22-22-220000-111-1-1-111-220000-2200000000-111-11-11-1000000−33−333−33−300000000
χ332-2-22-2-222-111-11-11-1-22-2200002-2-2222-2-21-100001-1−i3i3−i3i3i3−i3i3−i3-111-11-11-100−i3i3i3−i30000000000000000
χ342-2-22-2-222-111-11-11-1-22-2200002-2-2222-2-21-100001-1i3−i3i3−i3−i3i3−i3i3-111-11-11-100i3−i3−i3i30000000000000000
χ353333333333333333-1-1-1-1333300000000-1-11111-1-11111111100000000-1-1-1-1-1-1000000001111-1-1-1-1
χ363333333333333333-1-1-1-1333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111100000000-1-1-1-1-1-111
χ373333333333333333-1-1-1-1-3-3-3-300000000-1-11111-1-11111111100000000-1-1-1-1-1-100000000-1-1-1-11111
χ383333333333333333-1-1-1-1-3-3-3-300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111100000000111111-1-1
χ393333-3-3-3-33333-3-3-3-311-1-13i3i−3i−3i000000001111-1-1-1-11111-1-1-1-100000000-11-1-11100000000ii−i−i−ii−ii
χ403333-3-3-3-33333-3-3-3-311-1-13i3i−3i−3i0000000011-1-111-1-1-1-1-1-11111000000001-111-1-100000000−i−iii−iii−i
χ413333-3-3-3-33333-3-3-3-311-1-1−3i−3i3i3i000000001111-1-1-1-11111-1-1-1-100000000-11-1-11100000000−i−iiii−ii−i
χ423333-3-3-3-33333-3-3-3-311-1-1−3i−3i3i3i0000000011-1-111-1-1-1-1-1-11111000000001-111-1-100000000ii−i−ii−i−ii
χ4344444444-2-2-2-2-2-2-2-244440000-2-2-2-2-2-2-2-2-2-20000-2-200000000111111110000000000000000000000
χ444444-4-4-4-4-2-2-2-22222-4-4440000-2-2-2-22222220000-2-2000000001111-1-1-1-10000000000000000000000
χ4544-4-44i−4i4i−4i44-4-44i4i−4i−4i00004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ131-11-1−ii−ii00000000000000001-11-1−i−iii000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000
χ4644-4-44i−4i4i−4i44-4-44i4i−4i−4i0000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ131-11-1−ii−ii00000000000000001-11-1−i−iii000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000
χ4744-4-44i−4i4i−4i-2-222−2i−2i2i2i00000000-22-222i−2i2i−2i00−2i22i222−2200i2i2−i2−i2−2−2221-11-1−i−iii0000000000000000000000
χ4844-4-44i−4i4i−4i-2-222−2i−2i2i2i00000000-22-222i−2i2i−2i002i2−2i2−222200−i2−i2i2i222−2−21-11-1−i−iii0000000000000000000000
χ4944-4-4−4i4i−4i4i44-4-4−4i−4i4i4i0000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ231-11-1i−ii−i00000000000000001-11-1ii−i−i000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000
χ5044-4-4−4i4i−4i4i44-4-4−4i−4i4i4i00004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ231-11-1i−ii−i00000000000000001-11-1ii−i−i000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000
χ5144-4-4−4i4i−4i4i-2-2222i2i−2i−2i00000000-22-22−2i2i−2i2i00−2i22i2−222200i2i2−i2−i222−2−21-11-1ii−i−i0000000000000000000000
χ5244-4-4−4i4i−4i4i-2-2222i2i−2i−2i00000000-22-22−2i2i−2i2i002i2−2i222−2200−i2−i2i2i2−2−2221-11-1ii−i−i0000000000000000000000
χ534-44-44i−4i−4i4i4-44-44i−4i−4i4i0000000011-1-1i−i−ii000000000000000011-1-1−iii−i000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000
χ544-44-44i−4i−4i4i4-44-44i−4i−4i4i0000000011-1-1i−i−ii000000000000000011-1-1−iii−i000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000
χ554-44-44i−4i−4i4i4-44-44i−4i−4i4i00000000-2-222−2i2i2i−2i0000000000000000-2-2222i−2i−2i2i0000000000000000000000
χ564-44-44i−4i−4i4i-22-22−2i2i2i−2i00000000-2-222−2i2i2i−2i000000006−6−66i6−i6−i6i611-1-1−iii−i0000000000000000000000
χ574-44-44i−4i−4i4i-22-22−2i2i2i−2i00000000-2-222−2i2i2i−2i00000000−666−6−i6i6i6−i611-1-1−iii−i0000000000000000000000
χ584-44-4−4i4i4i−4i4-44-4−4i4i4i−4i0000000011-1-1−iii−i000000000000000011-1-1i−i−ii000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000
χ594-44-4−4i4i4i−4i4-44-4−4i4i4i−4i0000000011-1-1−iii−i000000000000000011-1-1i−i−ii000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000
χ604-44-4−4i4i4i−4i4-44-4−4i4i4i−4i00000000-2-2222i−2i−2i2i0000000000000000-2-222−2i2i2i−2i0000000000000000000000
χ614-44-4−4i4i4i−4i-22-222i−2i−2i2i00000000-2-2222i−2i−2i2i000000006−6−66−i6i6i6−i611-1-1i−i−ii0000000000000000000000
χ624-44-4−4i4i4i−4i-22-222i−2i−2i2i00000000-2-2222i−2i−2i2i00000000−666−6i6−i6−i6i611-1-1i−i−ii0000000000000000000000
χ634-4-4444-4-4-222-2-22-224-4-440000-222-222-2-2-2200002-2000000001-1-111-11-10000000000000000000000
χ644-4-44-4-444-222-22-22-2-44-440000-222-2-2-2222-200002-2000000001-1-11-11-110000000000000000000000
χ6566666666-3-3-3-3-3-3-3-3-2-2-2-200000000000011222211-1-1-1-1-1-1-1-100000000-2-211110000000000000000
χ6666666666-3-3-3-3-3-3-3-3-2-2-2-200000000000011-2-2-2-211111111110000000022-1-1-1-10000000000000000
χ676666-6-6-6-6-3-3-3-3333322-2-2000000000000-1-122-2-211-1-1-1-1111100000000-2211-1-10000000000000000
χ686666-6-6-6-6-3-3-3-3333322-2-2000000000000-1-1-2-222111111-1-1-1-1000000002-2-1-1110000000000000000
χ696-6-6666-6-66-6-666-66-6-222-2000000000000-2200002-200000000000000000000000000000000000000
χ706-6-6666-6-6-333-3-33-33-222-20000000000001-10000-11−i3i3−i3i3−i3i3−i3i30000000000i3−i3i3−i30000000000000000
χ716-6-6666-6-6-333-3-33-33-222-20000000000001-10000-11i3−i3i3−i3i3−i3i3−i30000000000−i3i3−i3i30000000000000000
χ726-6-66-6-6666-6-66-66-662-22-20000000000002-200002-200000000000000000000000000000000000000
χ736-6-66-6-666-333-33-33-32-22-2000000000000-110000-11−i3i3−i3i3i3−i3i3−i30000000000i3−i3−i3i30000000000000000
χ746-6-66-6-666-333-33-33-32-22-2000000000000-110000-11i3−i3i3−i3−i3i3−i3i30000000000−i3i3i3−i30000000000000000
χ7588-8-88i−8i8i−8i-4-444−4i−4i4i4i000000002-22-2−2i2i−2i2i0000000000000000-11-11ii−i−i0000000000000000000000
χ7688-8-8−8i8i−8i8i-4-4444i4i−4i−4i000000002-22-22i−2i2i−2i0000000000000000-11-11−i−iii0000000000000000000000
χ778-88-88i−8i−8i8i-44-44−4i4i4i−4i0000000022-2-22i−2i−2i2i0000000000000000-1-111i−i−ii0000000000000000000000
χ788-88-8−8i8i8i−8i-44-444i−4i−4i4i0000000022-2-2−2i2i2i−2i0000000000000000-1-111−iii−i0000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.