Finite Group Databasebeta

← Group #11864164

Character table — Group #11864164

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222244444444444444444888888888888888888888888121212121212121218181818181824242424242424242424242436484848487272
order122233444466666623666121212121212121212121212666688121224242424242424242424242424242424222244442222442244666612121212466121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-11-11-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-11-11-1-111-1-111-1-11-11-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1-1-11-1111
χ71111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-11-1-1-111-1-111-11-11-111
χ81111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1
χ9111111-1-111111111-11111-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-111111-1-1-1-111-1-111-1
χ10111111-1-111111111-11111-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-1-111-111-1-1-11
χ11111111-1-111111111-11111-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1-111-11
χ12111111-1-111111111-11111-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-111111-111-11-1
χ13111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-111-11111-1-1-1-11-111-1-11
χ14111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-11111-1-1-1-111-1-1-1111-1
χ15111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-111-1-11-1
χ16111111-1-111111111-11111-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1111111-1-11-11
χ1722222222-2-2222222-222222222-2-2-2-2-2-2-2-2-2-2-2-2002200000000000000000000000022-2-222000000000000-2000000
χ1822222222-2-2222222-222222222-2-2-2-2-2-2-2-2-2-2-2-20022000000000000000000000000-2-222-2-20000000000002000000
χ19222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200-2-20000000000000000000000002222-2-2000000000000-2000000
χ20222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222200-2-2000000000000000000000000-2-2-2-2220000000000002000000
χ2122222-122222-12-12-12-1-1-1-122-1-122-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-100220022000000020200-1-100-1-100-10-100
χ2222222-122222-12-12-12-1-1-1-122-1-122-1-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-100-2-200-2-20000000-20-2001100110010100
χ2322222-122222-12-12-12-1-1-1-122-1-122-1-1-1-1-1-12-1-1-1-2-2-1-1-2-2111111-2-2111111002200220000000-20-200-1-100-1-10010100
χ2422222-122222-12-12-12-1-1-1-122-1-122-1-1-1-1-1-12-1-1-1-2-2-1-1-2-2111111-2-211111100-2-200-2-200000002020011001100-10-100
χ2522222-1-2-2222-12-12-1-2-1-1-1-1-2-21122-1-1-1-1-1-1-21112-21122-1-1-1-1-1-1-2-2111111002200-2-20000000-20200-1-100110010-100
χ2622222-1-2-2222-12-12-1-2-1-1-1-1-2-21122-1-1-1-1-1-1-21112-21122-1-1-1-1-1-1-2-211111100-2-20022000000020-2001100-1-100-10100
χ2722222-1-2-2222-12-12-1-2-1-1-1-1-2-21122-1-1-1-1-1-1-2111-2211-2-211111122-1-1-1-1-1-1002200-2-2000000020-200-1-1001100-10100
χ2822222-1-2-2222-12-12-1-2-1-1-1-1-2-21122-1-1-1-1-1-1-2111-2211-2-211111122-1-1-1-1-1-100-2-200220000000-202001100-1-10010-100
χ292222-122222-12-12-122-1-1-1-1-1-122-1-122-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1220022000000002020-1-100-1-1000-10-1000
χ302222-122222-12-12-122-1-1-1-1-1-122-1-122-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-200-2-200000000-20-20110011000101000
χ312222-122222-12-12-122-1-1-1-1-1-122-1-122-1-1-1-1-12-1-1-2-2-1-111-2-2111111-2-2111122002200000000-20-20-1-100-1-1000101000
χ322222-122222-12-12-122-1-1-1-1-1-122-1-122-1-1-1-1-12-1-1-2-2-1-111-2-2111111-2-21111-2-200-2-2000000002020110011000-10-1000
χ332222-12-2-222-12-12-12-2-1-1-1-111-2-2-1-122-1-1-1-11-2112-211-1-122-1-1-1-111-2-211112200-2-20000000020-20-1-10011000-101000
χ342222-12-2-222-12-12-12-2-1-1-1-111-2-2-1-122-1-1-1-11-2112-211-1-122-1-1-1-111-2-21111-2-2002200000000-20201100-1-100010-1000
χ352222-12-2-222-12-12-12-2-1-1-1-111-2-2-1-122-1-1-1-11-211-221111-2-21111-1-122-1-1-1-12200-2-200000000-2020-1-1001100010-1000
χ362222-12-2-222-12-12-12-2-1-1-1-111-2-2-1-122-1-1-1-11-211-221111-2-21111-1-122-1-1-1-1-2-200220000000020-201100-1-1000-101000
χ372-2-2222002-2-2-2-2-22202-2-2200002-22-222-2-20000000000000000000000002-200002-2002-22-200002-200002-20000000
χ382-2-2222002-2-2-2-2-22202-2-2200002-22-222-2-20000000000000000000000002-20000-2200-22-2200002-20000-220000000
χ392-2-2222002-2-2-2-2-22202-2-2200002-22-222-2-2000000000000000000000000-2200002-200-22-220000-2200002-20000000
χ402-2-2222002-2-2-2-2-22202-2-2200002-22-222-2-2000000000000000000000000-220000-22002-22-20000-220000-220000000
χ412-2-222200-22-2-2-2-22202-2-220000-22-22-2-222000000000000000000000000002-22-200002-2-220000002-22-2000000000
χ422-2-222200-22-2-2-2-22202-2-220000-22-22-2-222000000000000000000000000002-2-220000-222-20000002-2-22000000000
χ432-2-222200-22-2-2-2-22202-2-220000-22-22-2-22200000000000000000000000000-222-20000-222-2000000-222-2000000000
χ442-2-222200-22-2-2-2-22202-2-220000-22-22-2-22200000000000000000000000000-22-2200002-2-22000000-22-22000000000
χ4544444-244-4-44-24-24-2-4-2-2-2-244-2-2-4-4222222-422200-2-20000000000000000000000000000000000000000000000000
χ4644444-2-4-4-4-44-24-24-24-2-2-2-2-4-422-4-42222224-2-2-200220000000000000000000000000000000000000000000000000
χ474444-2444-4-4-24-24-24-4-2-2-2-2-2-24422-4-422222-42200-2-20000000000000000000000000000000000000000000000000
χ484444-24-4-4-4-4-24-24-244-2-2-2-222-4-422-4-42222-24-2-200220000000000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-241111-2-2-2-2-2-2-2-21111-2-2114411-2-2-2-21111-2-2-2-21111000000000000000000000000000000000
χ504444-2-24444-2-2-2-2-2-241111-2-2-2-2-2-2-2-21111-2-211-4-4112222-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ514444-2-244-4-4-2-2-2-2-2-2-41111-2-2-2-22222-1-1-1-122-1-1001100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000000
χ524444-2-244-4-4-2-2-2-2-2-2-41111-2-2-2-22222-1-1-1-122-1-100110000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000000
χ534444-2-2-4-444-2-2-2-2-2-2-411112222-2-2-2-2111122-1-14-4-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000000
χ544444-2-2-4-444-2-2-2-2-2-2-411112222-2-2-2-2111122-1-1-44-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-24111122222222-1-1-1-1-2-21100-1-100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-24111122222222-1-1-1-1-2-21100-1-10000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000000
χ5744-4-4444i−4i0044-4-4-4-4044-4-44i−4i4i−4i000000000000004i−4i0000000000000000000000000000000000000000000000000
χ5844-4-444−4i4i0044-4-4-4-4044-4-4−4i4i−4i4i00000000000000−4i4i0000000000000000000000000000000000000000000000000
χ5944-4-44-24i−4i004-2-42-420-2-2224i−4i−2i2i00000000000000−2i2i006−66−66−600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ6044-4-44-24i−4i004-2-42-420-2-2224i−4i−2i2i00000000000000−2i2i00−66−66−6600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ6144-4-44-2−4i4i004-2-42-420-2-222−4i4i2i−2i000000000000002i−2i006−66−66−600−i6i6−i6i6−i6i6000000000000000000000000000000000
χ6244-4-44-2−4i4i004-2-42-420-2-222−4i4i2i−2i000000000000002i−2i00−66−66−6600i6−i6i6−i6i6−i6000000000000000000000000000000000
χ6344-4-4-244i−4i00-242-42-40-2-222−2i2i4i−4i00000000000000−2i2ii6−i600i6−i6−i6i66−600−666−6000000000000000000000000000000000
χ6444-4-4-244i−4i00-242-42-40-2-222−2i2i4i−4i00000000000000−2i2i−i6i600−i6i6i6−i6−66006−6−66000000000000000000000000000000000
χ6544-4-4-24−4i4i00-242-42-40-2-2222i−2i−4i4i000000000000002i−2ii6−i600i6−i6−i6i6−66006−6−66000000000000000000000000000000000
χ6644-4-4-24−4i4i00-242-42-40-2-2222i−2i−4i4i000000000000002i−2i−i6i600−i6i6i6−i66−600−666−6000000000000000000000000000000000
χ6744-4-4-2-24i−4i00-2-22222011-1-1−2i2i−2i2i00003i−3i3i−3i003-300i−ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ6844-4-4-2-24i−4i00-2-22222011-1-1−2i2i−2i2i00003i−3i3i−3i003-300i−i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ6944-4-4-2-24i−4i00-2-22222011-1-1−2i2i−2i2i0000−3i3i−3i3i00-3300i−ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ7044-4-4-2-24i−4i00-2-22222011-1-1−2i2i−2i2i0000−3i3i−3i3i00-3300i−i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ7144-4-4-2-2−4i4i00-2-22222011-1-12i−2i2i−2i00003i−3i3i−3i00-3300−iii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000000
χ7244-4-4-2-2−4i4i00-2-22222011-1-12i−2i2i−2i00003i−3i3i−3i00-3300−ii−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ7344-4-4-2-2−4i4i00-2-22222011-1-12i−2i2i−2i0000−3i3i−3i3i003-300−iii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ7444-4-4-2-2−4i4i00-2-22222011-1-12i−2i2i−2i0000−3i3i−3i3i003-300−ii−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ754-44-4440000-4-444-4-404-44-4000000000000000000000000000000000000000000004-400000000000000000000000
χ764-44-4440000-4-444-4-404-44-400000000000000000000000000000000000000000000-4400000000000000000000000
χ774-4-444-2004-4-42-424-20-222-200004-4-22-2-2220000000000000000000000000000004-40000000000000000-220000000
χ784-4-444-2004-4-42-424-20-222-200004-4-22-2-222000000000000000000000000000000-4400000000000000002-20000000
χ794-4-444-200-44-42-424-20-222-20000-442-222-2-2000000000000000000000000004-40000000000000000-2200000000000
χ804-4-444-200-44-42-424-20-222-20000-442-222-2-200000000000000000000000000-4400000000000000002-200000000000
χ814-4-44-24004-42-42-4-240-222-20000-224-4-2-2220000000000000000000000004-40000000000000000-220000000000000
χ824-4-44-24004-42-42-4-240-222-20000-224-4-2-222000000000000000000000000-4400000000000000002-20000000000000
χ834-4-44-2400-442-42-4-240-222-200002-2-4422-2-200000000000000000000000000004-40000000000000000-22000000000
χ844-4-44-2400-442-42-4-240-222-200002-2-4422-2-20000000000000000000000000000-4400000000000000002-2000000000
χ858-88-88-40000-848-4-840-44-44000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-4800004-8-484-80-44-44000000000000000000000000000000000000000000000000000000000000000000000
χ878-88-8-4-4000044-4-44402-22-2000000006i−6i−6i6i000000000000000000000000000000000000000000000000000000000
χ888-88-8-4-4000044-4-44402-22-200000000−6i6i6i−6i000000000000000000000000000000000000000000000000000000000
χ898-8-88-4-4008-84444-4-402-2-220000-44-4422-2-2000000000000000000000000000000000000000000000000000000000
χ908-8-88-4-400-884444-4-402-2-2200004-44-4-2-222000000000000000000000000000000000000000000000000000000000

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