Finite Group Databasebeta

← Group #11889724

Character table — Group #11889724

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122222222222244444444444444444888888888888888888888888121212122424242424242424242424242424363636363636363648484848
order122222334466666634666666612121212121212126688121212122424242424242424242424242424242422442444446666121212122444888812121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1-111111-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-111-1-1-1-1-111111111-1-1-1-111-1-1
χ811111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1-1111-1-111-1-1-11-1111-1-1-11-11
χ101111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-11-111-1-1-1-1111-11-1-1-111-111-1
χ111111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-11-1-11111-1-11-11-1-1-1111-1-11
χ121111-1-111111111111-1-1-1-1-111111111111-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-111-1-111-11-1111-1-11-11-1
χ131111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-11-11-111-1-11-11-1
χ141111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111111-1-1-1-111-11-11-1-1111-1-11
χ151111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1-1-1-1-11111-1-1-11-11-1-111-111-1
χ161111-1-111111111111-1-1-1-1-111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1111-11-111-1-1-11-11
χ1722222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-2000000000000000000000000000000000022-2-200000000
χ1822222222-2-22222222-22222222-2-2-2-2-2-2-2-22200-2-2-2-20000000000000000000000000000000000-2-22200000000
χ192222222-1222-1-12-12-1222-1-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12200220200-1-1-1-1000000000000-1-100
χ202222222-1222-1-12-12-1222-1-1-1-1-122-1-1-1-1-1-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-20-20011110000000000001100
χ212222222-1222-1-12-12-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-211111122002-20-200-1-1-1-10000000000001100
χ222222222-1222-1-12-12-1222-1-1-1-1-122-1-1-1-1-1-1-1-1-2-22-1-1-1-2-2111111-2-2111111-2-200-2202001111000000000000-1-100
χ23222222-1222-122-12-1-12-1-122-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100220020220000-1-1-1-10000000000-1-1
χ24222222-1222-122-12-1-12-1-122-1-1-1-1-122-1-1-1-1-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-200-20-2-200001111000000000011
χ25222222-1222-122-12-1-12-1-122-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-21111002200-202-20000-1-1-1-1000000000011
χ26222222-1222-122-12-1-12-1-122-1-1-1-1-122-1-1-1-1-1-1-2-2-12-1-111-2-2111111-2-2111100-2-20020-22000011110000000000-1-1
χ272222-2-222-2-222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-200222200000000000000000000000000000000002-2-2200000000
χ282222-2-222-2-222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-20022220000000000000000000000000000000000-222-200000000
χ292222-2-22-1222-1-12-12-1-2-2-211-1-1-122-1-1-1-1-1-1112-2-211122-1-1-1-1-1-1-2-21111112200-220-200-1-1110000000000001-100
χ302222-2-22-1222-1-12-12-1-2-2-211-1-1-122-1-1-1-1-1-1112-2-211122-1-1-1-1-1-1-2-2111111-2-2002-2020011-1-1000000000000-1100
χ312222-2-22-1222-1-12-12-1-2-2-211-1-1-122-1-1-1-1-1-111-22-2111-2-211111122-1-1-1-1-1-12200-2-20200-1-111000000000000-1100
χ322222-2-22-1222-1-12-12-1-2-2-211-1-1-122-1-1-1-1-1-111-22-2111-2-211111122-1-1-1-1-1-1-2-200220-20011-1-10000000000001-100
χ332222-2-2-1222-122-12-1-1-211-2-2-1-1-1-1-122-1-1-1-1112-21-211-1-122-1-1-1-111-2-21111002200-20-220000-1-11100000000001-1
χ342222-2-2-1222-122-12-1-1-211-2-2-1-1-1-1-122-1-1-1-1112-21-211-1-122-1-1-1-111-2-2111100-2-200202-2000011-1-10000000000-11
χ352222-2-2-1222-122-12-1-1-211-2-2-1-1-1-1-122-1-1-1-111-221-21111-2-21111-1-122-1-1-1-100220020-2-20000-1-1110000000000-11
χ362222-2-2-1222-122-12-1-1-211-2-2-1-1-1-1-122-1-1-1-111-221-21111-2-21111-1-122-1-1-1-100-2-200-2022000011-1-100000000001-1
χ372-22-200222-2-2-2-222-2200000-2-222-22-222-2-20000000000000000000000002-22i−2i0000002-2002i−2i0000002i−2i000000
χ382-22-200222-2-2-2-222-2200000-2-222-22-222-2-20000000000000000000000002-2−2i2i0000002-200−2i2i000000−2i2i000000
χ392-22-200222-2-2-2-222-2200000-2-222-22-222-2-2000000000000000000000000-222i−2i000000-22002i−2i000000−2i2i000000
χ402-22-200222-2-2-2-222-2200000-2-222-22-222-2-2000000000000000000000000-22−2i2i000000-2200−2i2i0000002i−2i000000
χ414444444-2-4-44-2-24-24-2-444-2-2-2-2-2-4-4222222-2-200-42220000000000000000000000000000000000000000000000
χ42444444-24-4-4-244-24-2-2-4-2-244-2-2-222-4-42222-2-2002-4220000000000000000000000000000000000000000000000
χ43444444-2-244-2-2-2-2-2-214-2-2-2-2111-2-2-2-211111144-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000
χ44444444-2-244-2-2-2-2-2-214-2-2-2-2111-2-2-2-2111111-4-4-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000
χ45444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2-21112222-1-1-1-1110022-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000
χ46444444-2-2-4-4-2-2-2-2-2-21-4-2-2-2-21112222-1-1-1-1110022-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000
χ474444-4-44-2-4-44-2-24-24-24-4-422-2-2-2-4-422222222004-2-2-20000000000000000000000000000000000000000000000
χ484444-4-4-24-4-4-244-24-2-2422-4-4-2-2-222-4-422222200-24-2-20000000000000000000000000000000000000000000000
χ494444-4-4-2-244-2-2-2-2-2-21-42222111-2-2-2-21111-1-14-422-1-1-2-2-2-211112222-1-1-1-1000000000000000000000000000000
χ504444-4-4-2-244-2-2-2-2-2-21-42222111-2-2-2-21111-1-1-4422-1-12222-1-1-1-1-2-2-2-21111000000000000000000000000000000
χ514444-4-4-2-2-4-4-2-2-2-2-2-21422221112222-1-1-1-1-1-100-2-21100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ524444-4-4-2-2-4-4-2-2-2-2-2-21422221112222-1-1-1-1-1-100-2-2110000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ5344-4-44-4440044-4-4-4-4404-44-44-4-4000000004-40000000000000000000000000000000000000000000000000000
χ5444-4-44-44-2004-22-42-4-204-4-22-22200000000-22000000006−66−66−6006−66−66−6000000000000000000000000000000
χ5544-4-44-44-2004-22-42-4-204-4-22-22200000000-2200000000−66−66−6600−66−66−66000000000000000000000000000000
χ5644-4-44-4-2400-24-42-42-20-224-4-22200000000-22000000i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000000000
χ5744-4-44-4-2400-24-42-42-20-224-4-22200000000-22000000−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000000000
χ5844-4-44-4-2-200-2-2222210-22-221-1-100003i−3i3i−3i1-100003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ5944-4-44-4-2-200-2-2222210-22-221-1-100003i−3i3i−3i1-100003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ6044-4-44-4-2-200-2-2222210-22-221-1-10000−3i3i−3i3i1-10000−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ6144-4-44-4-2-200-2-2222210-22-221-1-10000−3i3i−3i3i1-10000−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ6244-4-4-44440044-4-4-4-440-44-444-4-400000000-440000000000000000000000000000000000000000000000000000
χ6344-4-4-444-2004-22-42-4-20-442-2-222000000002-2000000006−66−66−600−66−66−66000000000000000000000000000000
χ6444-4-4-444-2004-22-42-4-20-442-2-222000000002-200000000−66−66−66006−66−66−6000000000000000000000000000000
χ6544-4-4-44-2400-24-42-42-202-2-44-222000000002-2000000i6−i600i6−i6−i6i6−i6i600−i6i6i6−i6000000000000000000000000000000
χ6644-4-4-44-2400-24-42-42-202-2-44-222000000002-2000000−i6i600−i6i6i6−i6i6−i600i6−i6−i6i6000000000000000000000000000000
χ6744-4-4-44-2-200-2-22222102-22-21-1-100003i−3i3i−3i-110000−3i3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ6844-4-4-44-2-200-2-22222102-22-21-1-100003i−3i3i−3i-110000−3i3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ6944-4-4-44-2-200-2-22222102-22-21-1-10000−3i3i−3i3i-1100003i−3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ7044-4-4-44-2-200-2-22222102-22-21-1-10000−3i3i−3i3i-1100003i−3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ714-44-40044-44-4-4-444-4400000-4-44-44-44-4-444000000000000000000000000000000000000000000000000000000
χ724-44-4004-24-4-4224-2-4-20000022-24-4-22-2-2220000000000000000000000004-400000000-22000000000000000000
χ734-44-4004-24-4-4224-2-4-20000022-24-4-22-2-222000000000000000000000000-44000000002-2000000000000000000
χ744-44-4004-2-44-4224-2-4-20000022-2-442-222-2-2000000000000000000000000000000000000−2i32i30000000000000000
χ754-44-4004-2-44-4224-2-4-20000022-2-442-222-2-20000000000000000000000000000000000002i3−2i30000000000000000
χ764-44-400-244-42-4-4-242-20000022-2-224-4-2-222000000000000000000000000004i−4i0000000000−2i2i00000000000000
χ774-44-400-244-42-4-4-242-20000022-2-224-4-2-22200000000000000000000000000−4i4i00000000002i−2i00000000000000
χ784-44-400-24-442-4-4-242-20000022-22-2-4422-2-2000000000000000000000000000000000000000023−23000000000000
χ794-44-400-24-442-4-4-242-20000022-22-2-4422-2-20000000000000000000000000000000000000000−2323000000000000
χ804-4-44004400-4-44-4-44400000-44-40000000000000000000000000000000000000000000000000000000022−220000
χ814-4-44004400-4-44-4-44400000-44-400000000000000000000000000000000000000000000000000000000−22220000
χ828-88-800-4-48-8444-4-44200000-2-22-44-4422-2-2000000000000000000000000000000000000000000000000000000
χ838-88-800-4-4-88444-4-44200000-2-224-44-4-2-222000000000000000000000000000000000000000000000000000000
χ848-8-88008-400-84-4-848-4000004-4400000000000000000000000000000000000000000000000000000000000000
χ858-8-8800-48004-884-8-4-4000004-4400000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-40044-444-4200000-22-200006i−6i−6i6i000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-40044-444-4200000-22-20000−6i6i6i−6i000000000000000000000000000000000000000000000000000000

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