Finite Group Databasebeta

← Group #11794975

Character table — Group #11794975

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111224444444444448888888888812121212181818182424242424242424242424242424484848487272727272
order12442433666612121212121246121212121212121212888822442488882424242424242424612242444488
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111-11-1-1-1-11-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-111-1-1
χ6111111111111111111-11-1-1-1-11-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-111-1-1-111
χ7111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-111
χ8111111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-111-1-1
χ9222222222222222222222222222220000-2-2-2-2000000000000000000-20000
χ10222222222222222222-22-2-2-2-22-2-2-2-20000-2-2-2-200000000000000000020000
χ112222-2-2222-2-222222-2-20-20000-2000000002-2-2200000000000000000002i−2i00
χ122222-2-2222-2-222222-2-20-20000-2000000002-2-220000000000000000000−2i2i00
χ132222-2-2222-2-222222-2-20-20000-200000000-222-20000000000000000000002i−2i
χ142222-2-2222-2-222222-2-20-20000-200000000-222-2000000000000000000000−2i2i
χ1522-2-22-2222222-2-2-2-2-2-2020000-20000000022-2-200002i−2i00002i2i−2i−2i000000000
χ1622-2-22-2222222-2-2-2-2-2-2020000-20000000022-2-20000−2i2i0000−2i−2i2i2i000000000
χ1722-2-22-2222222-2-2-2-2-2-2020000-200002i2i−2i−2i-2-2220000002i2i−2i−2i0000000000000
χ1822-2-22-2222222-2-2-2-2-2-2020000-20000−2i−2i2i2i-2-222000000−2i−2i2i2i0000000000000
χ1922-2-2-22222-2-22-2-2-2-2220-200002000000002-22-2002i−2i0000000000002i−2i00000
χ2022-2-2-22222-2-22-2-2-2-2220-200002000000002-22-200−2i2i000000000000−2i2i00000
χ2122-2-2-22222-2-22-2-2-2-2220-20000200000000-22-222-20000000000002-20000000
χ2222-2-2-22222-2-22-2-2-2-2220-20000200000000-22-22-22000000000000-220000000
χ234444441-2111-211-2-2114-21111-2-2-2-2-222220000000022-1-1-1-1-1-1-1-1000000000
χ244444441-2111-211-2-2114-21111-2-2-2-2-2-2-2-2-200000000-2-211111111000000000
χ254444441-2111-211-2-211-4-2-1-1-1-1-22222222200000000-2-2-1-1-1-11111000000000
χ264444441-2111-211-2-211-4-2-1-1-1-1-22222-2-2-2-200000000221111-1-1-1-1000000000
χ27444444-21-2-2-21-2-211-2-241-2-2-2-2111110000000022220000000000-1-1-1-100000
χ28444444-21-2-2-21-2-211-2-241-2-2-2-21111100000000-2-2-2-20000000000111100000
χ29444444-21-2-2-21-2-211-2-2-4122221-1-1-1-10000000022-2-20000000000-1-11100000
χ30444444-21-2-2-21-2-211-2-2-4122221-1-1-1-100000000-2-222000000000011-1-100000
χ3144-4-44-41-2111-2-1-122-1-10-233-3-3200002i2i−2i−2i000000002i−2i−i−iii−i−iii000000000
χ3244-4-44-41-2111-2-1-122-1-10-233-3-320000−2i−2i2i2i00000000−2i2iii−i−iii−i−i000000000
χ3344-4-44-41-2111-2-1-122-1-10-2-3-333200002i2i−2i−2i00000000−2i2i−i−iiiii−i−i000000000
χ3444-4-44-41-2111-2-1-122-1-10-2-3-33320000−2i−2i2i2i000000002i−2iii−i−i−i−iii000000000
χ3544-4-4-44-21-222122-1-1-2-20-1000013i3i−3i−3i000000002-22i−2i0000000000-11−ii00000
χ3644-4-4-44-21-222122-1-1-2-20-1000013i3i−3i−3i00000000-22−2i2i00000000001-1i−i00000
χ3744-4-4-44-21-222122-1-1-2-20-100001−3i−3i3i3i000000002-2−2i2i0000000000-11i−i00000
χ3844-4-4-44-21-222122-1-1-2-20-100001−3i−3i3i3i00000000-222i−2i00000000001-1−ii00000
χ394-44i−4i001-2-13-32i−i2i−2i3i−3i00−i3i33−30−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000
χ404-44i−4i001-2-13-32i−i2i−2i3i−3i00−i3i33−30−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000
χ414-44i−4i001-2-13-32i−i2i−2i3i−3i00i3−i3−330ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000
χ424-44i−4i001-2-13-32i−i2i−2i3i−3i00i3−i3−330ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000
χ434-44i−4i0044-400-44i−4i−4i4i00000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000
χ444-44i−4i0044-400-44i−4i−4i4i0000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000
χ454-4−4i4i001-2-13-32−ii−2i2i−3i3i00−i3i3−330−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000
χ464-4−4i4i001-2-13-32−ii−2i2i−3i3i00−i3i3−330−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000
χ474-4−4i4i001-2-13-32−ii−2i2i−3i3i00i3−i33−30ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000
χ484-4−4i4i001-2-13-32−ii−2i2i−3i3i00i3−i33−30ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000
χ494-4−4i4i0044-400-4−4i4i4i−4i0000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000
χ504-4−4i4i0044-400-4−4i4i4i−4i00000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000
χ518888-8-82-42-2-2-422-4-4-2-2040000400000000000000000000000000000000000
χ528888-8-8-42-4442-4-422440-20000-200000000000000000000000000000000000
χ5388-8-88-8-42-4-4-4244-2-244020000-200000000000000000000000000000000000
χ5488-8-8-882-42-2-2-4-2-24422040000-400000000000000000000000000000000000
χ558-88i−8i002-4-2-6642i−2i4i−4i−6i6i000000000000000000000000000000000000000000
χ568-88i−8i00-42400-2−4i4i−2i2i0000−2i32i323−230ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000000
χ578-88i−8i00-42400-2−4i4i−2i2i00002i3−2i3−23230−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000000
χ588-8−8i8i002-4-2-664−2i2i−4i4i6i−6i000000000000000000000000000000000000000000
χ598-8−8i8i00-42400-24i−4i2i−2i0000−2i32i3−23230ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000000
χ608-8−8i8i00-42400-24i−4i2i−2i00002i3−2i323−230−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000000

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