Finite Group Databasebeta

← Group #11792425

Character table — Group #11792425

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1111224444444444448888888888812121212181818182424242424242424242424242424484848487272727272
order12442433666612121212121268122424242424242424224422442244668812122424242466121244448
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11
χ411111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111-11-1-1-1-1-1-1-1-1111111111-11-111-1-111-1-1-1-11-11-111-1-1-1
χ61111111111111111111-11-1-1-1-1-1-1-1-111111111-11-1111-1-111-1-1-1-1-11-11-1-111-1
χ71111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-111-1-111111-11-1-1-111-1
χ81111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-11111-11-1111-1-1-1
χ9222222222222222222222222222220000-2-2-2-20000000000000000000000-2
χ102222222222222222222-22-2-2-2-2-2-2-2-20000-2-2-2-200000000000000000000002
χ112222-2-222-2-22222-2-222-20-20000000000002-22-2000000000000000000002-20
χ122222-2-222-2-22222-2-222-20-20000000000002-22-200000000000000000000-220
χ132222-2-222-2-22222-2-222-20-2000000000000-22-220000000000000000002-2000
χ142222-2-222-2-22222-2-222-20-2000000000000-22-22000000000000000000-22000
χ1522-2-22-2222222-2-2-2-2-2-220-2000000000000-2-2220000002i−2i002i2i−2i−2i000000000
χ1622-2-22-2222222-2-2-2-2-2-220-2000000000000-2-222000000−2i2i00−2i−2i2i2i000000000
χ1722-2-22-2222222-2-2-2-2-2-220-20000000022-2-222-2-200002200-2-20000000000000
χ1822-2-22-2222222-2-2-2-2-2-220-200000000-2-22222-2-20000-2-200220000000000000
χ1922-2-2-2222-2-222-2-222-2-2-2020000000000002-2-22020-20000000000020-200000
χ2022-2-2-2222-2-222-2-222-2-2-2020000000000002-2-220-20200000000000-20200000
χ2122-2-2-2222-2-222-2-222-2-2-202000000000000-222-220-20000000000020-2000000
χ2222-2-2-2222-2-222-2-222-2-2-202000000000000-222-2-20200000000000-202000000
χ234444441-2111-2-2-21111-24-21111-2-2-2-2222200000000-1-122-1-1-1-1-1-1000000000
χ244444441-2111-2-2-21111-24-21111-2-2-2-2-2-2-2-20000000011-2-2111111000000000
χ254444441-2111-2-2-21111-2-4-2-1-1-1-12222222200000000-1-1-2-2-1-11111000000000
χ264444441-2111-2-2-21111-2-4-2-1-1-1-12222-2-2-2-200000000112211-1-1-1-1000000000
χ27444444-21-2-2-2111-2-2-2-2141-2-2-2-211110000000022220000000000-1-1-1-100000
χ28444444-21-2-2-2111-2-2-2-2141-2-2-2-2111100000000-2-2-2-20000000000111100000
χ29444444-21-2-2-2111-2-2-2-21-412222-1-1-1-1000000002-22-20000000000-11-1100000
χ30444444-21-2-2-2111-2-2-2-21-412222-1-1-1-100000000-22-2200000000001-11-100000
χ3144-4-44-41-2111-222-1-1-1-1-2023i3i−3i−3i000022-2-200000000-1-12i−2i11−i−iii000000000
χ3244-4-44-41-2111-222-1-1-1-1-2023i3i−3i−3i0000-2-2220000000011−2i2i-1-1ii−i−i000000000
χ3344-4-44-41-2111-222-1-1-1-1-202−3i−3i3i3i000022-2-200000000-1-1−2i2i11ii−i−i000000000
χ3444-4-44-41-2111-222-1-1-1-1-202−3i−3i3i3i0000-2-22200000000112i−2i-1-1−i−iii000000000
χ3544-4-4-44-2122-21-1-1-2-222-101000033-3-30000000022-2-20000000000-1-11100000
χ3644-4-4-44-2122-21-1-1-2-222-101000033-3-300000000-2-222000000000011-1-100000
χ3744-4-4-44-2122-21-1-1-2-222-1010000-3-333000000002-2-220000000000-111-100000
χ3844-4-4-44-2122-21-1-1-2-222-1010000-3-33300000000-222-200000000001-1-1100000
χ394-44i−4i001-23-3-122i−2i3i−3ii−i000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i62-22i−2i000000001-100i−i−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000
χ404-44i−4i001-23-3-122i−2i3i−3ii−i000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6-22−2i2i00000000-1100−iiζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000
χ414-44i−4i001-23-3-122i−2i3i−3ii−i000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−i6i62-22i−2i000000001-100i−iζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000
χ424-44i−4i001-23-3-122i−2i3i−3ii−i000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6-22−2i2i00000000-1100−ii−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000
χ434-44i−4i004400-4-4−4i4i004i−4i000000000002-22i−2i00000000-2200−2i2i0000000000000
χ444-44i−4i004400-4-4−4i4i004i−4i00000000000-22−2i2i000000002-2002i−2i0000000000000
χ454-4−4i4i001-23-3-12−2i2i−3i3i−ii000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−i6i62-2−2i2i000000001-100−iiζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000
χ464-4−4i4i001-23-3-12−2i2i−3i3i−ii000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6-222i−2i00000000-1100i−i−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000
χ474-4−4i4i001-23-3-12−2i2i−3i3i−ii000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66i6−i62-2−2i2i000000001-100−ii−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000
χ484-4−4i4i001-23-3-12−2i2i−3i3i−ii000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6-222i−2i00000000-1100i−iζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000
χ494-4−4i4i004400-4-44i−4i00−4i4i000000000002-2−2i2i00000000-22002i−2i0000000000000
χ504-4−4i4i004400-4-44i−4i00−4i4i00000000000-222i−2i000000002-200−2i2i0000000000000
χ518888-8-82-4-2-22-4-4-4-2-222404000000000000000000000000000000000000000
χ528888-8-8-4244-422244-4-4-20-2000000000000000000000000000000000000000
χ5388-8-88-8-42-4-4-42-2-2444420-2000000000000000000000000000000000000000
χ5488-8-8-882-4-2-22-44422-2-240-4000000000000000000000000000000000000000
χ558-88i−8i002-4-66-244i−4i−6i6i2i−2i000000000000000000000000000000000000000000
χ568-88i−8i00-42004-2−2i2i00−4i4i0002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23−66−i6i60000000000000000000000000000000
χ578-88i−8i00-42004-2−2i2i00−4i4i000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ236−6i6−i60000000000000000000000000000000
χ588-8−8i8i002-4-66-24−4i4i6i−6i−2i2i000000000000000000000000000000000000000000
χ598-8−8i8i00-42004-22i−2i004i−4i000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13−66i6−i60000000000000000000000000000000
χ608-8−8i8i00-42004-22i−2i004i−4i0002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ136−6−i6i60000000000000000000000000000000

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