Finite Group Databasebeta

← Group #10699220

Character table — Group #10699220

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212128888121224242424242424244488121212122424242444448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ9222222222-222-2222-2-2-222222-2-2-22-20000-2-200000000000000000000000022-2-2000000
χ10222222222-222-2222-2-2-222222-2-2-22-20000-2-2000000000000000000000000-2-222000000
χ112222222-2-22-2-222222-2-222-2-2-2222-220000-2-2000000000000000000000000000000002-2
χ122222222-2-22-2-222222-2-222-2-2-2222-220000-2-200000000000000000000000000000000-22
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-200002200000000002i−2i00002i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000220000000000−2i2i0000−2i−2i2i2i00000000000000
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
χ19222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-13333−3−3−3−3002i−2i−i3−i3i3i3−i−iii00000000000000
χ20222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-13333−3−3−3−300−2i2ii3i3−i3−i3ii−i−i00000000000000
χ21222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-1−3−3−3−33333002i−2ii3i3−i3−i3−i−iii00000000000000
χ22222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111110000-1-1−3−3−3−3333300−2i2i−i3−i3i3i3ii−i−i00000000000000
χ232222-2-22222-2-22222-22-2-2-22-2-22-2-22200002-2000000002-2002-22-2000000000000000000
χ242222-2-22222-2-22222-22-2-2-22-2-22-2-22200002-200000000-2200-22-22000000000000000000
χ252222-2-2222-2-2-2-22222-22-2-22-2-2-2222-20000-22000000000000000000002i2i−2i−2i0000000000
χ262222-2-2222-2-2-2-22222-22-2-22-2-2-2222-20000-2200000000000000000000−2i−2i2i2i0000000000
χ272222-2-22-2-22222222-2-22-2-2-2222-2-2-220000-22000000000000000000000000000022-2-200
χ282222-2-22-2-22222222-2-22-2-2-2222-2-2-220000-220000000000000000000000000000-2-22200
χ292222-2-22-2-2-222-222222-2-2-2-222-222-2-22i2i−2i−2i2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ302222-2-22-2-2-222-222222-2-2-2-222-222-2-2−2i−2i2i2i2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
χ312222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11−i3−i3i3i3i3i3−i3−i32-200-11-11−i3i3−i3i300000000000000
χ322222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11−i3−i3i3i3i3i3−i3−i3-22001-11-1i3−i3i3−i300000000000000
χ332222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11i3i3−i3−i3−i3−i3i3i32-200-11-11i3−i3i3−i300000000000000
χ342222-2-2-1222-2-22-1-1-1-22-211-111-111-1-10000-11i3i3−i3−i3−i3−i3i3i3-22001-11-1−i3i3−i3i300000000000000
χ352222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-1112i2i−2i−2i-11−i−iii−i−iii0000−i3i3i3−i33−3−3300000000000000
χ362222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-1112i2i−2i−2i-11−i−iii−i−iii0000i3−i3−i3i3−333−300000000000000
χ372222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-111−2i−2i2i2i-11ii−i−iii−i−i0000−i3i3i3−i3−333−300000000000000
χ382222-2-2-1-2-2-222-2-1-1-122-2111-1-11-1-111−2i−2i2i2i-11ii−i−iii−i−i0000i3−i3−i3i33−3−3300000000000000
χ392-2-222-22-2202-202-2-20002-2-22-200020−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000000000000002-2−i2i2−i2i200
χ402-2-222-22-2202-202-2-20002-2-22-200020−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000000000-22i2−i2i2−i200
χ412-2-222-22-2202-202-2-20002-2-22-200020i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000000000000002-2i2−i2i2−i200
χ422-2-222-22-2202-202-2-20002-2-22-200020i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000000000-22−i2i2−i2i200
χ432-2-22-2222-202-202-2-2000-2222-2000-202−2−22002−2−222−2−2200000000000000002i−2i00−i2i2i2−i200
χ442-2-22-2222-202-202-2-2000-2222-2000-202−2−22002−2−222−2−220000000000000000−2i2i00i2−i2−i2i200
χ452-2-22-2222-202-202-2-2000-2222-2000-20−222−200−222−2−222−200000000000000002i−2i00i2−i2−i2i200
χ462-2-22-2222-202-202-2-2000-2222-2000-20−222−200−222−2−222−20000000000000000−2i2i00−i2i2i2−i200
χ47444444-244-444-4-2-2-2-4-4-4-2-2-2-2-2222-220000220000000000000000000000000000000000
χ48444444-2-4-44-4-44-2-2-24-4-4-2-2222-2-2-22-20000220000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-24-4422-2222-2-2-2200002-20000000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-2-4-44222-2-2-2222-200002-20000000000000000000000000000000000
χ5144-4-400400400-4-44-4000000004000-4000000000000000000000000002-22-20000000000
χ5244-4-400400400-4-44-4000000004000-400000000000000000000000000-22-220000000000
χ5344-4-400400-4004-44-400000000-40004000000000000000000000000002i−2i−2i2i0000000000
χ5444-4-400400-4004-44-400000000-4000400000000000000000000000000−2i2i2i−2i0000000000
χ554-4-444-444-40-4404-4-40004-44-44000-400000000000000000000000000000000000000000
χ564-4-444-4-24-40-440-222000-22-22-200020000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000
χ574-4-444-4-24-40-440-222000-22-22-200020000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000
χ584-4-444-4-2-4404-40-222000-222-22000-20−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ594-4-444-4-2-4404-40-222000-222-22000-202i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ604-4-44-444-440-4404-4-4000-44-4-44000400000000000000000000000000000000000000000
χ614-4-44-44-24-404-40-2220002-2-2-220002022−22−222200−222−2−222−200000000000000000000000000
χ624-4-44-44-24-404-40-2220002-2-2-2200020−222222−22002−2−222−2−2200000000000000000000000000
χ634-4-44-44-2-440-440-2220002-222-2000-200000006−6−66−666−600000000000000000000000000
χ644-4-44-44-2-440-440-2220002-222-2000-20000000−666−66−6−6600000000000000000000000000
χ6588-8-800-400800-84-4400000000-400040000000000000000000000000000000000000000
χ6688-8-800-400-80084-44000000004000-40000000000000000000000000000000000000000
χ678-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-88-800-400000044-400000000043−43000000000000000000000000000000000000000000
χ698-88-800-400000044-4000000000−4343000000000000000000000000000000000000000000

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