Finite Group Databasebeta

← Group #10697689

Character table — Group #10697689

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888888888242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-11-11
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-11-11
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-11-1
χ9222222222-222-2-2-2222-2-22222-2-2-222-20000-2-2000000000000000000000000000022-2-20000
χ10222222222-222-2-2-2222-2-22222-2-2-222-20000-2-20000000000000000000000000000-2-2220000
χ112222222-2-22-2-2222222-2-222-2-2222-2-2222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ122222222-2-22-2-2222222-2-222-2-2222-2-22-2-222-2-2-2-2-2-222220000000000000000000000000000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000022000000002i2i2i2i−2i−2i−2i−2i00000000000000000000
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200002200000000−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ19222222-1-2-22-2-2222-1-1-1-2-2-1-111-1-1-111-122-2-211-1-1-1-1111100000000000033−3−333−3−300000000
χ20222222-1-2-22-2-2222-1-1-1-2-2-1-111-1-1-111-122-2-211-1-1-1-11111000000000000−3−333−3−33300000000
χ21222222-1-2-22-2-2222-1-1-1-2-2-1-111-1-1-111-1-2-222111111-1-1-1-100000000000033−3−3−3−33300000000
χ22222222-1-2-22-2-2222-1-1-1-2-2-1-111-1-1-111-1-2-222111111-1-1-1-1000000000000−3−33333−3−300000000
χ232222-2-222-222-22-2-22222-2-2-22-22-2-22-2200002-200000000000000000000000000000000020-2
χ242222-2-222-222-22-2-22222-2-2-22-22-2-22-2200002-2000000000000000000000000000000000-202
χ252222-2-222-2-22-2-222222-22-2-22-2-2222-2-20000-2200000000000000002-2002-22-2000000000000
χ262222-2-222-2-22-2-222222-22-2-22-2-2222-2-20000-220000000000000000-2200-22-22000000000000
χ272222-2-22-222-222-2-2222-22-2-2-222-2-2-2220000-220000000000000000000000000000000020-20
χ282222-2-22-222-222-2-2222-22-2-2-222-2-2-2220000-2200000000000000000000000000000000-2020
χ292222-2-22-22-2-22-2222222-2-2-2-22-222-22-200002-20000000000000000002-200002-22-200000000
χ302222-2-22-22-2-22-2222222-2-2-2-22-222-22-200002-2000000000000000000-220000-22-2200000000
χ312222-2-2-12-2-22-2-222-1-1-1-2211-111-1-1-11100001-133−3−333−3−3000000002-200-11-113−3−3300000000
χ322222-2-2-12-2-22-2-222-1-1-1-2211-111-1-1-11100001-133−3−333−3−300000000-22001-11-1−333−300000000
χ332222-2-2-12-2-22-2-222-1-1-1-2211-111-1-1-11100001-1−3−333−3−333000000002-200-11-11−333−300000000
χ342222-2-2-12-2-22-2-222-1-1-1-2211-111-1-1-11100001-1−3−333−3−33300000000-22001-11-13−3−3300000000
χ352222-2-2-1-22-2-22-222-1-1-12-2111-11-1-11-110000-1133−3−3−3−33300000000002-2−333−3-11-1100000000
χ362222-2-2-1-22-2-22-222-1-1-12-2111-11-1-11-110000-1133−3−3−3−3330000000000-223−3−331-11-100000000
χ372222-2-2-1-22-2-22-222-1-1-12-2111-11-1-11-110000-11−3−33333−3−300000000002-23−3−33-11-1100000000
χ382222-2-2-1-22-2-22-222-1-1-12-2111-11-1-11-110000-11−3−33333−3−30000000000-22−333−31-11-100000000
χ3922-2-22-22220-2-20002-2-2002-222000-2-202−22−2002−22−22−22−222−2−222−2−20000000000002-2000000
χ4022-2-22-22220-2-20002-2-2002-222000-2-202−22−2002−22−22−22−2−2−222−2−222000000000000-22000000
χ4122-2-22-22220-2-20002-2-2002-222000-2-20−22−2200−22−22−22−2222−2−222−2−2000000000000-22000000
χ4222-2-22-22220-2-20002-2-2002-222000-2-20−22−2200−22−22−22−22−2−222−2−2220000000000002-2000000
χ4322-2-22-22-2-20220002-2-2002-2-2-20002202−2−22002−22−2−22−22−i2−i2i2i2i2i2−i2−i2000000000000002i−2i0000
χ4422-2-22-22-2-20220002-2-2002-2-2-20002202−2−22002−22−2−22−22i2i2−i2−i2−i2−i2i2i200000000000000−2i2i0000
χ4522-2-22-22-2-20220002-2-2002-2-2-2000220−222−200−22−222−22−2−i2−i2i2i2i2i2−i2−i200000000000000−2i2i0000
χ4622-2-22-22-2-20220002-2-2002-2-2-2000220−222−200−22−222−22−2i2i2−i2−i2−i2−i2i2i2000000000000002i−2i0000
χ47444444-244-444-4-4-4-2-2-2-4-4-2-2-2-2222-2-22000022000000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-4-4-2-2-244-2-2222222220000-2-2000000000000000000000000000000000000
χ494444-4-4-24-444-44-4-4-2-2-24-422-22-222-22-20000-22000000000000000000000000000000000000
χ504444-4-4-2-444-444-4-4-2-2-2-44222-2-2222-2-200002-2000000000000000000000000000000000000
χ5144-4-44-4-2440-4-4000-22200-22-2-200022022−2222−2200−22−22−22−220000000000000000000000000000
χ5244-4-44-4-2440-4-4000-22200-22-2-2000220−2222−2222002−22−22−22−20000000000000000000000000000
χ5344-4-44-4-2-4-4044000-22200-2222000-2-2022−22−222200−22−222−22−20000000000000000000000000000
χ5444-4-44-4-2-4-4044000-22200-2222000-2-20−222222−22002−22−2−22−220000000000000000000000000000
χ5544-4-4-4444-40-440004-4-400-444-4000-440000000000000000000000000000000000000000000
χ5644-4-4-444-4404-40004-4-400-44-440004-40000000000000000000000000000000000000000000
χ5744-4-4-44-24-40-44000-222002-2-220002-200000006−6−666−6−660000000000000000000000000000
χ5844-4-4-44-24-40-44000-222002-2-220002-20000000−666−6−666−60000000000000000000000000000
χ5944-4-4-44-2-4404-4000-222002-22-2000-2200000006−6−66−666−60000000000000000000000000000
χ6044-4-4-44-2-4404-4000-222002-22-2000-220000000−666−66−6−660000000000000000000000000000
χ614-44-400400400-400-44-400000040000-4000000000000002-22-22-22-200000000000000000000
χ624-44-400400400-400-44-400000040000-400000000000000-22-22-22-2200000000000000000000
χ634-44-400400-400400-44-4000000-400004000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ644-44-400400-400400-44-4000000-40000400000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ654-4-440040000004i−4i-4-4400000004i−4i000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ664-4-440040000004i−4i-4-4400000004i−4i00000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ674-4-44004000000−4i4i-4-440000000−4i4i00000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ684-4-44004000000−4i4i-4-440000000−4i4i000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ698-88-800-400800-8004-44000000-400004000000000000000000000000000000000000000000
χ708-88-800-400-8008004-4400000040000-4000000000000000000000000000000000000000000
χ718-8-8800-40000008i−8i44-40000000−4i4i000000000000000000000000000000000000000000000
χ728-8-8800-4000000−8i8i44-400000004i−4i000000000000000000000000000000000000000000000

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