Finite Group Databasebeta

← Group #10698903

Character table — Group #10698903

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888888888242424242424242422444488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ9222222222-2-2-22-22222-2-22222-2-2-222-20000-2-2000000000000000000000000000022-2-20000
χ10222222222-2-2-22-22222-2-22222-2-2-222-20000-2-20000000000000000000000000000-2-2220000
χ112222222-2-2222-22-2222-2-222-2-2222-2-220000-2-200000000000000002i−2i002i2i−2i−2i000000000000
χ122222222-2-2222-22-2222-2-222-2-2222-2-220000-2-20000000000000000−2i2i00−2i−2i2i2i000000000000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200002200000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-20000220000000000000000000000000000000000−2i2i
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
χ19222222-1-2-2222-22-2-1-1-1-2-2-1-111-1-1-111-1000011−i3−i3−i3−i3i3i3i3i3000000002i−2i00−i−iii33−3−300000000
χ20222222-1-2-2222-22-2-1-1-1-2-2-1-111-1-1-111-1000011−i3−i3−i3−i3i3i3i3i300000000−2i2i00ii−i−i−3−33300000000
χ21222222-1-2-2222-22-2-1-1-1-2-2-1-111-1-1-111-1000011i3i3i3i3−i3−i3−i3−i3000000002i−2i00−i−iii−3−33300000000
χ22222222-1-2-2222-22-2-1-1-1-2-2-1-111-1-1-111-1000011i3i3i3i3−i3−i3−i3−i300000000−2i2i00ii−i−i33−3−300000000
χ232222-2-222-222-22-2-22222-2-2-22-222-22-2-22i2i−2i−2i2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ242222-2-222-222-22-2-22222-2-2-22-222-22-2-2−2i−2i2i2i2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ252222-2-222-2-2-2222-2222-22-2-22-2-2-222-220000-22000000002222-2-2-2-200000000000000000000
χ262222-2-222-2-2-2222-2222-22-2-22-2-2-222-220000-2200000000-2-2-2-2222200000000000000000000
χ272222-2-22-2222-2-2-22222-22-2-2-2222-2-22-20000-220000000000000000002-200002-22-200000000
χ282222-2-22-2222-2-2-22222-22-2-2-2222-2-22-20000-22000000000000000000-220000-22-2200000000
χ292222-2-22-22-2-22-2222222-2-2-2-22-2-22-22200002-2000000000000000000000000000000002-200
χ302222-2-22-22-2-22-2222222-2-2-2-22-2-22-22200002-200000000000000000000000000000000-2200
χ312222-2-2-12-222-22-2-2-1-1-12-211-11-1-11-1112i2i−2i−2i-11−i−iii−i−iii000000000000−i3i3−i3i33−3−3300000000
χ322222-2-2-12-222-22-2-2-1-1-12-211-11-1-11-1112i2i−2i−2i-11−i−iii−i−iii000000000000i3−i3i3−i3−333−300000000
χ332222-2-2-12-222-22-2-2-1-1-12-211-11-1-11-111−2i−2i2i2i-11ii−i−iii−i−i000000000000−i3i3−i3i3−333−300000000
χ342222-2-2-12-222-22-2-2-1-1-12-211-11-1-11-111−2i−2i2i2i-11ii−i−iii−i−i000000000000i3−i3i3−i33−3−3300000000
χ352222-2-2-1-2222-2-2-22-1-1-1-22111-1-1-111-1100001-133−3−3−3−33300000000002-2−333−3-11-1100000000
χ362222-2-2-1-2222-2-2-22-1-1-1-22111-1-1-111-1100001-133−3−3−3−3330000000000-223−3−331-11-100000000
χ372222-2-2-1-2222-2-2-22-1-1-1-22111-1-1-111-1100001-1−3−33333−3−300000000002-23−3−33-11-1100000000
χ382222-2-2-1-2222-2-2-22-1-1-1-22111-1-1-111-1100001-1−3−33333−3−30000000000-22−333−31-11-100000000
χ3922-2-22-2222000-20-22-2-2002-222000-2-202−22−2002−22−22−22−222−2−222−2−20000000000002-2000000
χ4022-2-22-2222000-20-22-2-2002-222000-2-202−22−2002−22−22−22−2−2−222−2−222000000000000-22000000
χ4122-2-22-2222000-20-22-2-2002-222000-2-20−22−2200−22−22−22−2222−2−222−2−2000000000000-22000000
χ4222-2-22-2222000-20-22-2-2002-222000-2-20−22−2200−22−22−22−22−2−222−2−2220000000000002-2000000
χ4322-2-2-2222-2000-2022-2-200-222-2000-220−i2i2i2−i200−i2i2i2−i2−i2i2i2−i222−2−2−2−222000000000000002i−2i0000
χ4422-2-2-2222-2000-2022-2-200-222-2000-220−i2i2i2−i200−i2i2i2−i2−i2i2i2−i2−2−22222−2−200000000000000−2i2i0000
χ4522-2-2-2222-2000-2022-2-200-222-2000-220i2−i2−i2i200i2−i2−i2i2i2−i2−i2i222−2−2−2−22200000000000000−2i2i0000
χ4622-2-2-2222-2000-2022-2-200-222-2000-220i2−i2−i2i200i2−i2−i2i2i2−i2−i2i2−2−22222−2−2000000000000002i−2i0000
χ47444444-244-4-4-44-44-2-2-2-4-4-2-2-2-2222-2-22000022000000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-4-4-2-2-244-2-2222222220000-2-2000000000000000000000000000000000000
χ494444-4-4-24-4-4-4444-4-2-2-2-4422-2222-2-22-200002-2000000000000000000000000000000000000
χ504444-4-4-2-44-4-44-444-2-2-24-4222-222-22-2-20000-22000000000000000000000000000000000000
χ5144-4-44-44-4-40004044-4-4004-4-4-4000440000000000000000000000000000000000000000000
χ5244-4-44-4-244000-40-4-22200-22-2-200022022−2222−2200−22−22−22−220000000000000000000000000000
χ5344-4-44-4-244000-40-4-22200-22-2-2000220−2222−2222002−22−22−22−20000000000000000000000000000
χ5444-4-44-4-2-4-4000404-22200-2222000-2-20000000i6−i6i6−i6−i6i6−i6i60000000000000000000000000000
χ5544-4-44-4-2-4-4000404-22200-2222000-2-20000000−i6i6−i6i6i6−i6i6−i60000000000000000000000000000
χ5644-4-4-444-4400040-44-4-400-44-440004-40000000000000000000000000000000000000000000
χ5744-4-4-44-24-4000-404-222002-2-220002-20−2i22i22i2−2i200i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ5844-4-4-44-24-4000-404-222002-2-220002-202i2−2i2−2i22i200−i2i2i2−i2−i2i2i2−i20000000000000000000000000000
χ5944-4-4-44-2-4400040-4-222002-22-2000-2200000006−6−66−666−60000000000000000000000000000
χ6044-4-4-44-2-4400040-4-222002-22-2000-220000000−666−66−6−660000000000000000000000000000
χ614-44-4004004i−4i0000-44-40000004i−4i0000000000000000002-22-22i−2i2i−2i00000000000000000000
χ624-44-4004004i−4i0000-44-40000004i−4i000000000000000000-22-22−2i2i−2i2i00000000000000000000
χ634-44-400400−4i4i0000-44-4000000−4i4i0000000000000000002-22-2−2i2i−2i2i00000000000000000000
χ644-44-400400−4i4i0000-44-4000000−4i4i000000000000000000-22-222i−2i2i−2i00000000000000000000
χ654-4-44004000040-40-4-4400000000400-4000000000000000000−2i22i22i2−2i200000000000000000000
χ664-4-44004000040-40-4-4400000000400-40000000000000000002i2−2i2−2i22i200000000000000000000
χ674-4-440040000-4040-4-4400000000-40040000000000000022−22−2222000000000000000000000000
χ684-4-440040000-4040-4-4400000000-400400000000000000−222222−22000000000000000000000000
χ698-88-800-4008i−8i00004-44000000−4i4i0000000000000000000000000000000000000000000000
χ708-88-800-400−8i8i00004-440000004i−4i0000000000000000000000000000000000000000000000
χ718-8-8800-4000080-8044-400000000-4004000000000000000000000000000000000000000000
χ728-8-8800-40000-808044-400000000400-4000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).