Finite Group Databasebeta

← Group #10698814

Character table — Group #10698814

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242422448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ9222222222-2-222222-2-2-222222-2-2-2-220000-2-20000000000000000000022-2-20000000000
χ10222222222-2-222222-2-2-222222-2-2-2-220000-2-200000000000000000000-2-2220000000000
χ112222222-2-222-2-2222-22-222-2-2-222-2-2-20000-2200000000002i−2i00002i2i−2i−2i00000000000000
χ122222222-2-222-2-2222-22-222-2-2-222-2-2-20000-220000000000−2i2i0000−2i−2i2i2i00000000000000
χ132222222-2-2-2-2-2-22222-2222-2-2-2-2-222-200002-2000000000000000000000000000000002i−2i
χ142222222-2-2-2-2-2-22222-2222-2-2-2-2-222-200002-200000000000000000000000000000000−2i2i
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-100000000000000
χ19222222-1-2-222-2-2-1-1-1-22-2-1-1111-1-111100001-13333−3−3−3−3002i−2i−i3−i3i3i3−i−iii00000000000000
χ20222222-1-2-222-2-2-1-1-1-22-2-1-1111-1-111100001-13333−3−3−3−300−2i2ii3i3−i3−i3ii−i−i00000000000000
χ21222222-1-2-222-2-2-1-1-1-22-2-1-1111-1-111100001-1−3−3−3−33333002i−2ii3i3−i3−i3−i−iii00000000000000
χ22222222-1-2-222-2-2-1-1-1-22-2-1-1111-1-111100001-1−3−3−3−3333300−2i2i−i3−i3i3i3ii−i−i00000000000000
χ232222-2-222-2222-2222-2-22-2-222-22222-20000-2-200000000000000000000000022-2-2000000
χ242222-2-222-2222-2222-2-22-2-222-22222-20000-2-2000000000000000000000000-2-222000000
χ252222-2-222-2-2-22-222222-2-2-222-2-2-2-2-2-22i2i−2i−2i222i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ262222-2-222-2-2-22-222222-2-2-222-2-2-2-2-2-2−2i−2i2i2i22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ272222-2-22-2222-222222-2-2-2-2-2-2222-2-2200002-2000000000000000000000000000022-2-200
χ282222-2-22-2222-222222-2-2-2-2-2-2222-2-2200002-20000000000000000000000000000-2-22200
χ292222-2-22-22-2-2-22222-222-2-2-2-22-2-22220000-22000000002-2002-22-2000000000000000000
χ302222-2-22-22-2-2-22222-222-2-2-2-22-2-22220000-2200000000-2200-22-22000000000000000000
χ312222-2-2-12-2-2-22-2-1-1-122-211-1-11111112i2i−2i−2i-1-1−i−iii−i−iii0000−i3i3i3−i33−33−300000000000000
χ322222-2-2-12-2-2-22-2-1-1-122-211-1-11111112i2i−2i−2i-1-1−i−iii−i−iii0000i3−i3−i3i3−33−3300000000000000
χ332222-2-2-12-2-2-22-2-1-1-122-211-1-1111111−2i−2i2i2i-1-1ii−i−iii−i−i0000−i3i3i3−i3−33−3300000000000000
χ342222-2-2-12-2-2-22-2-1-1-122-211-1-1111111−2i−2i2i2i-1-1ii−i−iii−i−i0000i3−i3−i3i33−33−300000000000000
χ352222-2-2-1-22-2-2-22-1-1-1-2221111-111-1-1-100001-1−i3−i3i3i3i3i3−i3−i32-200-11-11−i3i3i3−i300000000000000
χ362222-2-2-1-22-2-2-22-1-1-1-2221111-111-1-1-100001-1−i3−i3i3i3i3i3−i3−i3-22001-11-1i3−i3−i3i300000000000000
χ372222-2-2-1-22-2-2-22-1-1-1-2221111-111-1-1-100001-1i3i3−i3−i3−i3−i3i3i32-200-11-11i3−i3−i3i300000000000000
χ382222-2-2-1-22-2-2-22-1-1-1-2221111-111-1-1-100001-1i3i3−i3−i3−i3−i3i3i3-22001-11-1−i3i3i3−i300000000000000
χ3922-2-22-222200-2-22-2-20002-22-220000-22−22−2002−22−22−22−20000000000002-2002−22−2000000
χ4022-2-22-222200-2-22-2-20002-22-220000-22−22−2002−22−22−22−2000000000000-2200−22−22000000
χ4122-2-22-222200-2-22-2-20002-22-220000-2−22−2200−22−22−22−220000000000002-200−22−22000000
χ4222-2-22-222200-2-22-2-20002-22-220000-2−22−2200−22−22−22−22000000000000-22002−22−2000000
χ4322-2-2-2222-200-222-2-2000-222-2-200002−i2i2i2−i200−i2i2i2−i2−i2i2i2−i2000000000000002i−2i2−2−22000000
χ4422-2-2-2222-200-222-2-2000-222-2-200002−i2i2i2−i200−i2i2i2−i2−i2i2i2−i200000000000000−2i2i−222−2000000
χ4522-2-2-2222-200-222-2-2000-222-2-200002i2−i2−i2i200i2−i2−i2i2i2−i2−i2i2000000000000002i−2i−222−2000000
χ4622-2-2-2222-200-222-2-2000-222-2-200002i2−i2−i2i200i2−i2−i2i2i2−i2−i2i200000000000000−2i2i2−2−22000000
χ47444444-244-4-444-2-2-2-4-4-4-2-2-2-2-22222-20000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-24-44-2-222222-2-220000-220000000000000000000000000000000000
χ494444-4-4-24-4444-4-2-2-2-4-4422-2-22-2-2-2-220000220000000000000000000000000000000000
χ504444-4-4-2-4444-44-2-2-24-4-42222-2-2-222-20000-220000000000000000000000000000000000
χ5144-4-44-44-4-400444-4-40004-4-44-4000040000000000000000000000000000000000000000
χ5244-4-44-4-24400-4-4-222000-22-22-20000222−2222−2200−22−22−22−2200000000000000000000000000
χ5344-4-44-4-24400-4-4-222000-22-22-200002−2222−2222002−22−22−22−200000000000000000000000000
χ5444-4-44-4-2-4-40044-222000-222-220000-20000006−66−6−66−6600000000000000000000000000
χ5544-4-44-4-2-4-40044-222000-222-220000-2000000−66−666−66−600000000000000000000000000
χ5644-4-4-444-44004-44-4-4000-44-4440000-40000000000000000000000000000000000000000
χ5744-4-4-44-24-400-44-2220002-2-2220000-2−2i22i22i2−2i200i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ5844-4-4-44-24-400-44-2220002-2-2220000-22i2−2i2−2i22i200−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ5944-4-4-44-2-44004-4-2220002-22-2-200002000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ6044-4-4-44-2-44004-4-2220002-22-2-200002000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ614-4-44004004-400-4-44000000004-400000000000000000000000000000000000000022−2200
χ624-4-44004004-400-4-44000000004-4000000000000000000000000000000000000000−222200
χ634-4-4400400-4400-4-4400000000-44000000000000000000000000000000000000022−220000
χ644-4-4400400-4400-4-4400000000-440000000000000000000000000000000000000−22220000
χ658-88-8008000000-88-800000000000000000000000000000000000000000000000000000
χ668-88-800-40000004-440000000000−4i34i300000000000000000000000000000000000000000
χ678-88-800-40000004-4400000000004i3−4i300000000000000000000000000000000000000000
χ688-8-8800-4008-80044-400000000-440000000000000000000000000000000000000000000
χ698-8-8800-400-880044-4000000004-40000000000000000000000000000000000000000000

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