Finite Group Databasebeta

← Group #11781683

Character table — Group #11781683

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222244444444444444444888888888888888888888888242424242424242424242424363636364848484848487272
order12223344446666663466612121212121212121212121288121212121212242424242424242424242424242424248888242424242424242488882466121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-11-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11111
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-111
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ92222222-2-222222222-222222-2-2-2-2-2-2-2-22200-2-222-2-2000000000000000000000000000000000000002-2
χ102222222-2-222222222-222222-2-2-2-2-2-2-2-22200-2-222-2-200000000000000000000000000000000000000-22
χ11222222-222-22222222-2222-2-222222222-2-200-2-2-2-2-2-2000000000000000000000000000022-2-200000000
χ12222222-222-22222222-2222-2-222222222-2-200-2-2-2-2-2-20000000000000000000000000000-2-22200000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-22i−2i22-2-2222i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i000000000000000000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2−2i2i22-2-222−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i000000000000000000000000
χ1522222-1222222-1-1-12-12-1-1-12-1-12-1-1-12-1-12-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12200-1-1-1-10000000020-1-10000
χ1622222-1222222-1-1-12-12-1-1-12-1-12-1-1-12-1-12-1222-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200111100000000-20110000
χ1722222-1222222-1-1-12-12-1-1-12-1-12-1-1-12-1-12-1-2-22-1-1-1-1-1-2-2111111-2-21111112200-1-1-1-100000000-20110000
χ1822222-1222222-1-1-12-12-1-1-12-1-12-1-1-12-1-12-1-2-22-1-1-1-1-1-2-2111111-2-2111111-2-20011110000000020-1-10000
χ1922222-1-2-2-2-222-1-1-12-12-1-1-1-211-2111-211-212i−2i2-111-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000033−3−30000000000−i3i30000
χ2022222-1-2-2-2-222-1-1-12-12-1-1-1-211-2111-211-212i−2i2-111-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0000−3−3330000000000i3−i30000
χ2122222-1-2-2-2-222-1-1-12-12-1-1-1-211-2111-211-21−2i2i2-111-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i000033−3−30000000000i3−i30000
χ2222222-1-2-2-2-222-1-1-12-12-1-1-1-211-2111-211-21−2i2i2-111-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0000−3−3330000000000−i3i30000
χ232222-122222-1-1222-1-12-1-1-1-122-1-1-12-1-1-1-1222-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100220000-1-1-1-100000200-1-100
χ242222-122222-1-1222-1-12-1-1-1-122-1-1-12-1-1-1-1222-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-20000111100000-2001100
χ252222-122222-1-1222-1-12-1-1-1-122-1-1-12-1-1-1-12-2-2-12-1-1-1-111-2-2111111-2-2111100220000-1-1-1-100000-2001100
χ262222-122222-1-1222-1-12-1-1-1-122-1-1-12-1-1-1-12-2-2-12-1-1-1-111-2-2111111-2-2111100-2-20000111100000200-1-100
χ272222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2111-21111-22i−2i-1211-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii0000000033−3−300000000−i3i300
χ282222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2111-21111-22i−2i-1211-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00000000−3−33300000000i3−i300
χ292222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2111-21111-2−2i2i-1211-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000033−3−300000000i3−i300
χ302222-12-2-2-2-2-1-1222-1-12-1-1-11-2-2111-21111-2−2i2i-1211-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00000000−3−33300000000−i3i300
χ3122-2-22202-20-2-22-2-22202-2-2002222-2-2-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-20000000000
χ3222-2-22202-20-2-22-2-22202-2-2002222-2-2-2-200000000000000000000000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2-220000000000
χ3322-2-22202-20-2-22-2-22202-2-2002222-2-2-2-200000000000000000000000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2-220000000000
χ3422-2-22202-20-2-22-2-22202-2-2002222-2-2-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-20000000000
χ3544444-24-4-4444-2-2-24-2-4-2-2-24-22-4222-4224-200-42-2-2220000000000000000000000000000000000000000
χ3644444-2-444-444-2-2-24-2-4-2-2-2-42-24-2-2-24-2-2-4200-4222220000000000000000000000000000000000000000
χ374444-244-4-44-2-2444-2-2-4-2-2-2-24-4222-4222-24002-4-2-2220000000000000000000000000000000000000000
χ384444-24-444-4-2-2444-2-2-4-2-2-22-44-2-2-24-2-2-22-4002-422220000000000000000000000000000000000000000
χ394444-2-24444-2-2-2-2-2-214111-2-2-2-211-2-211-2-244-2-21111-2-2-2-21111-2-2-2-21111000000000000000000000000
χ404444-2-24444-2-2-2-2-2-214111-2-2-2-211-2-211-2-2-4-4-2-211112222-1-1-1-12222-1-1-1-1000000000000000000000000
χ414444-2-24-4-44-2-2-2-2-2-21-4111-2-222-1-122-1-1-2-2002211-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000
χ424444-2-24-4-44-2-2-2-2-2-21-4111-2-222-1-122-1-1-2-2002211-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000
χ434444-2-2-444-4-2-2-2-2-2-21-411122-2-211-2-211220022-1-1-1-1000033-3-30000-3-333000000000000000000000000
χ444444-2-2-444-4-2-2-2-2-2-21-411122-2-211-2-211220022-1-1-1-10000-3-333000033-3-3000000000000000000000000
χ454444-2-2-4-4-4-4-2-2-2-2-2-2141112222-1-122-1-1224i−4i-2-2-1-111−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000
χ464444-2-2-4-4-4-4-2-2-2-2-2-2141112222-1-122-1-122−4i4i-2-2-1-1112i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000
χ4744-4-4440-440-4-44-4-44404-4-400-4-4-4-4444400000000000000000000000000000000000000000000000000
χ4844-4-44-204-40-4-4-2224-20-22200-24-2-22-42200000000000000000000000000−2i22i200i2−i2i2−i20000000000000000
χ4944-4-44-204-40-4-4-2224-20-22200-24-2-22-422000000000000000000000000002i2−2i200−i2i2−i2i20000000000000000
χ5044-4-44-20-440-4-4-2224-20-222002-422-24-2-2000000000000000000000000000000i6−i6−i6i60000000000000000
χ5144-4-44-20-440-4-4-2224-20-222002-422-24-2-2000000000000000000000000000000−i6i6i6−i60000000000000000
χ5244-4-4-2404-40224-4-4-2-20-222004-2-2-2-42220000000000000000000000000000−2i22i20000i2−i2i2−i2000000000000
χ5344-4-4-2404-40224-4-4-2-20-222004-2-2-2-422200000000000000000000000000002i2−2i20000−i2i2−i2i2000000000000
χ5444-4-4-240-440224-4-4-2-20-22200-42224-2-2-20000000000000000000000000000000000i6−i6−i6i6000000000000
χ5544-4-4-240-440224-4-4-2-20-22200-42224-2-2-20000000000000000000000000000000000−i6i6i6−i6000000000000
χ564-44-44400004-4-44-4-440-44-400000000000000000000000000000000000000000000000000−2i22i200000000
χ574-44-44400004-4-44-4-440-44-4000000000000000000000000000000000000000000000000002i2−2i200000000
χ584-4-4444400-4-44-4-44-440-4-444400000000-4-400004-4000000000000000000000000000000000000000000
χ594-4-4444-4004-44-4-44-440-4-44-4-400000000440000-44000000000000000000000000000000000000000000
χ604-4-444-2400-4-4422-2-4-2022-24-200000000-420000-2200006−66−66−6006−66−66−6000000000000000000000000
χ614-4-444-2400-4-4422-2-4-2022-24-200000000-420000-220000−66−66−6600−66−66−66000000000000000000000000
χ624-4-444-2-4004-4422-2-4-2022-2-42000000004-200002-20000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i6000000000000000000000000
χ634-4-444-2-4004-4422-2-4-2022-2-42000000004-200002-20000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i6000000000000000000000000
χ644-4-44-24400-42-2-4-442-2022-2-24000000002-40000-2200i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000
χ654-4-44-24400-42-2-4-442-2022-2-24000000002-40000-2200−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000
χ664-4-44-24-40042-2-4-442-2022-22-400000000-2400002-2006−6006−6−66−6600−666−6000000000000000000000000
χ674-4-44-24-40042-2-4-442-2022-22-400000000-2400002-200−6600−666−66−6006−6−66000000000000000000000000
χ684-4-44-2-2400-42-222-2210-1-11-2-2003i−3i003i−3i2200001-13i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ694-4-44-2-2400-42-222-2210-1-11-2-2003i−3i003i−3i2200001-13i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ704-4-44-2-2400-42-222-2210-1-11-2-200−3i3i00−3i3i2200001-1−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ714-4-44-2-2400-42-222-2210-1-11-2-200−3i3i00−3i3i2200001-1−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ724-4-44-2-2-40042-222-2210-1-1122003i−3i003i−3i-2-20000-11−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ734-4-44-2-2-40042-222-2210-1-1122003i−3i003i−3i-2-20000-11−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ744-4-44-2-2-40042-222-2210-1-112200−3i3i00−3i3i-2-20000-113i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ754-4-44-2-2-40042-222-2210-1-112200−3i3i00−3i3i-2-20000-113i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ7688-8-8-4-408-8044-444-4202-2-200-4-42244-2-200000000000000000000000000000000000000000000000000
χ7788-8-8-4-40-88044-444-4202-2-20044-2-2-4-42200000000000000000000000000000000000000000000000000
χ788-88-88-400008-84-44-8-404-44000000000000000000000000000000000000000000000000000000000000
χ798-88-8-480000-44-88-84-404-44000000000000000000000000000000000000000000000000000000000000
χ808-88-8-4-40000-444-44420-22-200006i−6i00−6i6i00000000000000000000000000000000000000000000000000
χ818-88-8-4-40000-444-44420-22-20000−6i6i006i−6i00000000000000000000000000000000000000000000000000

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