Finite Group Databasebeta

← Group #11776582

Character table — Group #11776582

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888181824242424242424242424242424242424363636484848487272
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242422222288882424242424242424444666688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-111-1-1
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11111
χ9111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i111-11-1i−ii−iii−i−iii−i−i1-1-11-11-1i−i
χ10111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-11-11−ii−ii−i−iii−i−iii1-1-1-11-11i−i
χ11111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-11-1-11i−i−iiii−i−i−i−iii-1111-1-11−ii
χ12111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−i1111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-111-1−iii−i−i−iiiii−i−i-111-111-1−ii
χ13111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii111-11-1−ii−ii−i−iii−i−iii1-1-11-11-1−ii
χ14111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-11-11i−ii−iii−i−iii−i−i1-1-1-11-11−ii
χ15111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-11-1-11−iii−i−i−iiiii−i−i-1111-1-11i−i
χ16111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii1111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-111-1i−i−iiii−i−i−i−iii-111-111-1i−i
χ172222222-2-222222222-222222-2-2222222-2-200-2-2-2-2-2-20000000000000000220000000000000000-22-2000000
χ182222222-2-222222222-222222-2-2222222-2-200-2-2-2-2-2-20000000000000000-2-200000000000000002-22000000
χ19222222-222-22222222-2222-2-222-2-2-2-2-2-22200-2-2-2-2220000000000000000220000000000000000-2-22000000
χ20222222-222-22222222-2222-2-222-2-2-2-2-2-22200-2-2-2-2220000000000000000-2-2000000000000000022-2000000
χ2122222-12222222-1-1-1-12-1-1-12-12-1-1-12-1-1-12-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100002200220000-1-1-1-100000-1-100
χ2222222-12222222-1-1-1-12-1-1-12-12-1-1-12-1-1-12-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-200-2-200001111000001100
χ2322222-12222222-1-1-1-12-1-1-12-12-1-1-12-1-1-12-1-2-22-1-1-1-1-1-2-2111111-2-211111100002200-2-20000111100000-1-100
χ2422222-12222222-1-1-1-12-1-1-12-12-1-1-12-1-1-12-1-2-22-1-1-1-1-1-2-2111111-2-21111110000-2-200220000-1-1-1-1000001100
χ2522222-1-2-2-2-2222-1-1-1-12-1-1-1-21-2111-2111-212i−2i2-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00002-2002i−2i0000−i−iii00000-1100
χ2622222-1-2-2-2-2222-1-1-1-12-1-1-1-21-2111-2111-212i−2i2-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii0000-2200−2i2i0000ii−i−i000001-100
χ2722222-1-2-2-2-2222-1-1-1-12-1-1-1-21-2111-2111-21−2i2i2-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00002-200−2i2i0000ii−i−i00000-1100
χ2822222-1-2-2-2-2222-1-1-1-12-1-1-1-21-2111-2111-21−2i2i2-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i0000-22002i−2i0000−i−iii000001-100
χ292222-122222-1-1-1222-12-1-1-1-12-12-1-1-12-1-1-1222-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10022002200-1-1-1-10000000-1-10000
χ302222-122222-1-1-1222-12-1-1-1-12-12-1-1-12-1-1-1222-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-200-2-20011110000000110000
χ312222-122222-1-1-1222-12-1-1-1-12-12-1-1-12-1-1-12-2-2-12-1-1-1-111-2-2111111-2-21111002200-2-20011110000000-1-10000
χ322222-122222-1-1-1222-12-1-1-1-12-12-1-1-12-1-1-12-2-2-12-1-1-1-111-2-2111111-2-2111100-2-2002200-1-1-1-10000000110000
χ332222-12-2-2-2-2-1-1-1222-12-1-1-11-21-2111-2111-22i−2i-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii002-2002i−2i00−i−iii0000000-110000
χ342222-12-2-2-2-2-1-1-1222-12-1-1-11-21-2111-2111-22i−2i-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii00-2200−2i2i00ii−i−i00000001-10000
χ352222-12-2-2-2-2-1-1-1222-12-1-1-11-21-2111-2111-2−2i2i-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i002-200−2i2i00ii−i−i0000000-110000
χ362222-12-2-2-2-2-1-1-1222-12-1-1-11-21-2111-2111-2−2i2i-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i00-22002i−2i00−i−iii00000001-10000
χ3744444-24-4-44444-2-2-2-2-4-2-2-24-2-42-2-24-2-2-2-4200-4222220000000000000000000000000000000000000000000
χ3844444-2-444-4444-2-2-2-2-4-2-2-2-424-222-42224-200-4222-2-20000000000000000000000000000000000000000000
χ394444-244-4-44-2-2-2444-2-4-2-2-2-242-4-2-2-24-2-22-4002-422220000000000000000000000000000000000000000000
χ404444-24-444-4-2-2-2444-2-4-2-2-22-4-24222-422-24002-422-2-20000000000000000000000000000000000000000000
χ414444-2-24444-2-2-2-2-2-214111-2-2-2-211-2-211-2-244-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000000
χ424444-2-24444-2-2-2-2-2-214111-2-2-2-211-2-211-2-2-4-4-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000000
χ434444-2-24-4-44-2-2-2-2-2-21-4111-2-22211-2-211220022-1-1-1-1000033-3-3000033-3-3000000000000000000000000000
χ444444-2-24-4-44-2-2-2-2-2-21-4111-2-22211-2-211220022-1-1-1-10000-3-3330000-3-333000000000000000000000000000
χ454444-2-2-444-4-2-2-2-2-2-21-411122-2-2-1-122-1-1-2-20022-1-11100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000
χ464444-2-2-444-4-2-2-2-2-2-21-411122-2-2-1-122-1-1-2-20022-1-1110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000
χ474444-2-2-4-4-4-4-2-2-2-2-2-2141112222-1-122-1-1224i−4i-2-211-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000
χ484444-2-2-4-4-4-4-2-2-2-2-2-2141112222-1-122-1-122−4i4i-2-211-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000
χ4944-4-44400004-4-44-4-4404-4-40000000000000000000000000000000000004-40000000000000000000000000
χ5044-4-44400004-4-44-4-4404-4-4000000000000000000000000000000000000-440000000000000000000000000
χ514-44-44404-40-44-4-44-440-44-4004-4000000-440000004-40000000000000000000000000000000000000000000
χ524-44-4440-440-44-4-44-440-44-400-440000004-4000000-440000000000000000000000000000000000000000000
χ534-44-44-204-40-44-42-22-202-220042000000-4-2000000-2200i6−i6i6−i6i6−i600i6−i6i6−i6i6−i6000000000000000000000000000
χ544-44-44-204-40-44-42-22-202-220042000000-4-2000000-2200−i6i6−i6i6−i6i600−i6i6−i6i6−i6i6000000000000000000000000000
χ554-44-44-20-440-44-42-22-202-2200-4-2000000420000002-2006−66−66−600−66−66−66000000000000000000000000000
χ564-44-44-20-440-44-42-22-202-2200-4-2000000420000002-200−66−66−66006−66−66−6000000000000000000000000000
χ574-44-4-2404-402-22-44-4-202-2200-2-400000024000000-226−6006−6−666−600−666−6000000000000000000000000000
χ584-44-4-2404-402-22-44-4-202-2200-2-400000024000000-22−6600−666−6−66006−6−66000000000000000000000000000
χ594-44-4-240-4402-22-44-4-202-220024000000-2-40000002-2i6−i600i6−i6−i6i6−i6i600i6−i6−i6i6000000000000000000000000000
χ604-44-4-240-4402-22-44-4-202-220024000000-2-40000002-2−i6i600−i6i6i6−i6i6−i600−i6i6i6−i6000000000000000000000000000
χ614-44-4-2-204-402-222-2210-11-100-223i−3i003i−3i2-200003i−3i1-16−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ624-44-4-2-204-402-222-2210-11-100-223i−3i003i−3i2-200003i−3i1-1−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ634-44-4-2-204-402-222-2210-11-100-22−3i3i00−3i3i2-20000−3i3i1-16−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ644-44-4-2-204-402-222-2210-11-100-22−3i3i00−3i3i2-20000−3i3i1-1−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ654-44-4-2-20-4402-222-2210-11-1002-23i−3i003i−3i-220000−3i3i-11i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ664-44-4-2-20-4402-222-2210-11-1002-23i−3i003i−3i-220000−3i3i-11−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ674-44-4-2-20-4402-222-2210-11-1002-2−3i3i00−3i3i-2200003i−3i-11i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ684-44-4-2-20-4402-222-2210-11-1002-2−3i3i00−3i3i-2200003i−3i-11−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ694-4-4444400-4-4-44-4-4440-4-44-4-400-4-4444400000000000000000000000000000000000000000000000000000
χ704-4-4444-4004-4-44-4-4440-4-44440044-4-4-4-400000000000000000000000000000000000000000000000000000
χ714-4-444-2400-4-4-4422-2-2022-2-4200224-2-2-20000000000000000000000000000000000000000i6−i6i6−i6000000000
χ724-4-444-2400-4-4-4422-2-2022-2-4200224-2-2-20000000000000000000000000000000000000000−i6i6−i6i6000000000
χ734-4-444-2-4004-4-4422-2-2022-24-200-2-2-422200000000000000000000000000000000000000006−6−66000000000
χ744-4-444-2-4004-4-4422-2-2022-24-200-2-2-42220000000000000000000000000000000000000000−666−6000000000
χ754-4-44-24400-422-2-4-44-2022-22-40022-24-2-2000000000000000000000000000000000000i6−i6i6−i60000000000000
χ764-4-44-24400-422-2-4-44-2022-22-40022-24-2-2000000000000000000000000000000000000−i6i6−i6i60000000000000
χ774-4-44-24-400422-2-4-44-2022-2-2400-2-22-4220000000000000000000000000000000000006−6−660000000000000
χ784-4-44-24-400422-2-4-44-2022-2-2400-2-22-422000000000000000000000000000000000000−666−60000000000000
χ7988-8-88-400008-8-8-444-40-444000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-480000-4448-8-8-40-444000000000000000000000000000000000000000000000000000000000000000
χ8188-8-8-4-40000-444-444202-2-200006i−6i00−6i6i00000000000000000000000000000000000000000000000000000
χ8288-8-8-4-40000-444-444202-2-20000−6i6i006i−6i00000000000000000000000000000000000000000000000000000
χ838-8-88-4-4800-844-444-420-2-224400-2-2-4-42200000000000000000000000000000000000000000000000000000
χ848-8-88-4-4-800844-444-420-2-22-4-4002244-2-200000000000000000000000000000000000000000000000000000

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