Finite Group Databasebeta

← Group #11782405

Character table — Group #11782405

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222244444444444444444888888888888888888888888242424242424242424242424363636364848484848487272
order1222334444666666346661212121212121212121212128812121212121224242424242424242424242424242424888824242424242424248888441212121244
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
χ922222222-2-22222222-222222-2-2-2-2-2-2-2-22200-2-222-2-2000000000000000000000000000000000000002-2
χ1022222222-2-22222222-222222-2-2-2-2-2-2-2-22200-2-222-2-200000000000000000000000000000000000000-22
χ11222222-2-2222222222-2222-2-222222222-2-200-2-2-2-2-2-2000000000000000000000000000022-2-200000000
χ12222222-2-2222222222-2222-2-222222222-2-200-2-2-2-2-2-20000000000000000000000000000-2-22200000000
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
χ1522222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12200-1-1-1-10000000020-1-10000
χ1622222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200111100000000-20110000
χ1722222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-1-2-2-12-1-1-1-1-2-2111111-2-21111112200-1-1-1-100000000-20110000
χ1822222-1222222-1-12-1-12-1-1-12-12-1-1-12-1-1-12-1-2-2-12-1-1-1-1-2-2111111-2-2111111-2-20011110000000020-1-10000
χ1922222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-212i−2i-1211-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii000033−3−30000000000−i3i30000
χ2022222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-212i−2i-1211-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0000−3−3330000000000i3−i30000
χ2122222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-21−2i2i-1211-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i000033−3−30000000000i3−i30000
χ2222222-1-2-2-2-222-1-12-1-12-1-1-1-21-2111-2111-21−2i2i-1211-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i0000−3−3330000000000−i3i30000
χ232222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100220000-1-1-1-100000200-1-100
χ242222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-12222-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-20000111100000-2001100
χ252222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-12-2-22-1-1-1-1-111-2-2111111-2-2111100220000-1-1-1-100000-2001100
χ262222-122222-1-122-12-12-1-1-1-12-12-1-1-12-1-1-12-2-22-1-1-1-1-111-2-2111111-2-2111100-2-20000111100000200-1-100
χ272222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-22i−2i2-111-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii0000000033−3−300000000−i3i300
χ282222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-22i−2i2-111-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii00000000−3−33300000000i3−i300
χ292222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-2−2i2i2-111-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000033−3−300000000i3−i300
χ302222-12-2-2-2-2-1-122-12-12-1-1-11-21-2111-2111-2−2i2i2-111-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i00000000−3−33300000000−i3i300
χ3122-2-22200-222-2-2-2-22202-2-200-2-2-2-22222000000000000000000000000002−2−i2i22−22−2−i2i2−i2i22i−2i0000000000
χ3222-2-22200-222-2-2-2-22202-2-200-2-2-2-22222000000000000000000000000002−2i2−i22−22−2i2−i2i2−i2−2i2i0000000000
χ3322-2-22200-222-2-2-2-22202-2-200-2-2-2-2222200000000000000000000000000−22−i2i2−22−22−i2i2−i2i2−2i2i0000000000
χ3422-2-22200-222-2-2-2-22202-2-200-2-2-2-2222200000000000000000000000000−22i2−i2−22−22i2−i2i2−i22i−2i0000000000
χ3544444-244-4-444-2-24-2-2-4-2-2-24-2-4222-42224-2002-4-2-2220000000000000000000000000000000000000000
χ3644444-2-4-44444-2-24-2-2-4-2-2-2-424-2-2-24-2-2-2-42002-422220000000000000000000000000000000000000000
χ374444-2444-4-4-2-244-24-2-4-2-2-2-242-4222-422-2400-42-2-2220000000000000000000000000000000000000000
χ384444-24-4-444-2-244-24-2-4-2-2-22-4-24-2-2-24-2-22-400-4222220000000000000000000000000000000000000000
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
χ414444-2-244-4-4-2-2-2-2-2-21-4111-2-222-1-122-1-1-2-2002211-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000
χ424444-2-244-4-4-2-2-2-2-2-21-4111-2-222-1-122-1-1-2-2002211-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000
χ434444-2-2-4-444-2-2-2-2-2-21-411122-2-211-2-211220022-1-1-1-1000033-3-30000-3-333000000000000000000000000
χ444444-2-2-4-444-2-2-2-2-2-21-411122-2-211-2-211220022-1-1-1-10000-3-333000033-3-3000000000000000000000000
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
χ4744-4-444004-44-4-4-4-44404-4-4004444-4-4-4-400000000000000000000000000000000000000000000000000
χ4844-4-44-2004-44-422-4-2-20-222004-2-2-2-42220000000000000000000000000000006−6−660000000000000000
χ4944-4-44-2004-44-422-4-2-20-222004-2-2-2-4222000000000000000000000000000000−666−60000000000000000
χ5044-4-44-200-444-422-4-2-20-22200-42224-2-2-20000000000000000000000000022−2200−22−220000000000000000
χ5144-4-44-200-444-422-4-2-20-22200-42224-2-2-200000000000000000000000000−2222002−22−20000000000000000
χ5244-4-4-24004-4-22-4-424-20-22200-24-2-22-4220000000000000000000000000000000000i6−i6−i6i6000000000000
χ5344-4-4-24004-4-22-4-424-20-22200-24-2-22-4220000000000000000000000000000000000−i6i6i6−i6000000000000
χ5444-4-4-2400-44-22-4-424-20-222002-422-24-2-20000000000000000000000000000−2i22i20000i2−i2i2−i2000000000000
χ5544-4-4-2400-44-22-4-424-20-222002-422-24-2-200000000000000000000000000002i2−2i20000−i2i2−i2i2000000000000
χ564-44-4444-400-444-4-4-440-44-44-400000000-4400004-4000000000000000000000000000000000000000000
χ574-44-444-4400-444-4-4-440-44-4-44000000004-40000-44000000000000000000000000000000000000000000
χ584-44-44-24-400-44-22-42-202-224200000000-4-20000-2200006−66−66−6006−66−66−6000000000000000000000000
χ594-44-44-24-400-44-22-42-202-224200000000-4-20000-220000−66−66−6600−66−66−66000000000000000000000000
χ604-44-44-2-4400-44-22-42-202-22-4-2000000004200002-20000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i6000000000000000000000000
χ614-44-44-2-4400-44-22-42-202-22-4-2000000004200002-20000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i6000000000000000000000000
χ624-44-4-244-4002-24-42-4-202-22-2-400000000240000-2200i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000
χ634-44-4-244-4002-24-42-4-202-22-2-400000000240000-2200−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000
χ644-44-4-24-44002-24-42-4-202-222400000000-2-400002-2006−6006−6−66−6600−666−6000000000000000000000000
χ654-44-4-24-44002-24-42-4-202-222400000000-2-400002-200−6600−666−66−6006−6−66000000000000000000000000
χ664-44-4-2-24-4002-2-222210-11-1-22003i−3i003i−3i2-200001-13i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ674-44-4-2-24-4002-2-222210-11-1-22003i−3i003i−3i2-200001-13i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ684-44-4-2-24-4002-2-222210-11-1-2200−3i3i00−3i3i2-200001-1−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ694-44-4-2-24-4002-2-222210-11-1-2200−3i3i00−3i3i2-200001-1−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ704-44-4-2-2-44002-2-222210-11-12-2003i−3i003i−3i-220000-11−3i3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ714-44-4-2-2-44002-2-222210-11-12-2003i−3i003i−3i-220000-11−3i3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ724-44-4-2-2-44002-2-222210-11-12-200−3i3i00−3i3i-220000-113i−3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000
χ734-44-4-2-2-44002-2-222210-11-12-200−3i3i00−3i3i-220000-113i−3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000
χ744-4-44440000-4-4-444-440-4-4400000000000000000000000000000000000000000000000000−2i22i200000000
χ754-4-44440000-4-4-444-440-4-44000000000000000000000000000000000000000000000000002i2−2i200000000
χ7688-8-8-4-4008-8-44444-4202-2-200-4-42244-2-200000000000000000000000000000000000000000000000000
χ7788-8-8-4-400-88-44444-4202-2-20044-2-2-4-42200000000000000000000000000000000000000000000000000
χ788-8-888-40000-8-84-484-4044-4000000000000000000000000000000000000000000000000000000000000
χ798-8-88-48000044-88-4-8-4044-4000000000000000000000000000000000000000000000000000000000000
χ808-8-88-4-40000444-4-4420-2-2200006i−6i00−6i6i00000000000000000000000000000000000000000000000000
χ818-8-88-4-40000444-4-4420-2-220000−6i6i006i−6i00000000000000000000000000000000000000000000000000

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