Finite Group Databasebeta

← Group #10714473

Character table — Group #10714473

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222224444444444444488888888888888161616161616161616161616242424242424242448484848
order1222223444466666888812121212242424241616161624244848484848484848448812121212242424242488161616164488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ92222222222222222-2-2-2-22222-2-2-2-20000-2-20000000000000000000022-2-200000000
χ102222222222222222-2-2-2-22222-2-2-2-20000-2-200000000000000000000-2-22200000000
χ112222222-2-2-2-2222220000-2-2-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i20000000000002-200−i2−i2i2i20000
χ122222222-2-2-2-2222220000-2-2-2-20000−i2−i2i2i200−i2−i2−i2−i2i2i2i2i2000000000000-2200i2i2−i2−i20000
χ132222222-2-2-2-2222220000-2-2-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i20000000000002-200i2i2−i2−i20000
χ142222222-2-2-2-2222220000-2-2-2-20000i2i2−i2−i200i2i2i2i2−i2−i2−i2−i2000000000000-2200−i2−i2i2i20000
χ15222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ18222222-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ192222-2-222-22-2222-2-22-22-22-22-222220000-2-20000000000000000000000000000002i−2i
χ202222-2-222-22-2222-2-22-22-22-22-222220000-2-2000000000000000000000000000000−2i2i
χ212222-2-222-22-2222-2-2-22-222-22-2-2-2-2-200002200000000002i−2i00002i2i−2i−2i000000000000
χ222222-2-222-22-2222-2-2-22-222-22-2-2-2-2-20000220000000000−2i2i0000−2i−2i2i2i000000000000
χ232222-2-2-12-22-2-1-1-111-22-22-11-1111110000-1-133−3−333−3−3002i−2i−i3−i3i3i3−i−iii000000000000
χ242222-2-2-12-22-2-1-1-111-22-22-11-1111110000-1-133−3−333−3−300−2i2ii3i3−i3−i3ii−i−i000000000000
χ252222-2-2-12-22-2-1-1-111-22-22-11-1111110000-1-1−3−333−3−333002i−2ii3i3−i3−i3−i−iii000000000000
χ262222-2-2-12-22-2-1-1-111-22-22-11-1111110000-1-1−3−333−3−33300−2i2i−i3−i3i3i3ii−i−i000000000000
χ272-2-222-2222-2-2-2-222-200002-2-2200002−22−2002−22−22−22−2000000000000002i−2i−i2i2−i2i20000
χ282-2-222-2222-2-2-2-222-200002-2-2200002−22−2002−22−22−22−200000000000000−2i2ii2−i2i2−i20000
χ292-2-222-2222-2-2-2-222-200002-2-220000−22−2200−22−22−22−22000000000000002i−2ii2−i2i2−i20000
χ302-2-222-2222-2-2-2-222-200002-2-220000−22−2200−22−22−22−2200000000000000−2i2i−i2i2−i2i20000
χ312-2-222-22-2-222-2-222-222-2-2-222-222-2-22i−2i−2i2i2-22i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ322-2-222-22-2-222-2-222-222-2-2-222-222-2-2−2i2i2i−2i2-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ332-2-222-22-2-222-2-222-2-2-222-222-2-2-2220000-220000000000000000000000002-2-220000
χ342-2-222-22-2-222-2-222-2-2-222-222-2-2-2220000-22000000000000000000000000-222-20000
χ352-2-222-2-1-2-22211-1-1122-2-21-1-11-1-1112i−2i−2i2i-11−ii−iii−ii−i0000−i3i3−i3i33−33−3000000000000
χ362-2-222-2-1-2-22211-1-1122-2-21-1-11-1-1112i−2i−2i2i-11−ii−iii−ii−i0000i3−i3i3−i3−33−33000000000000
χ372-2-222-2-1-2-22211-1-1122-2-21-1-11-1-111−2i2i2i−2i-11i−ii−i−ii−ii0000−i3i3−i3i3−33−33000000000000
χ382-2-222-2-1-2-22211-1-1122-2-21-1-11-1-111−2i2i2i−2i-11i−ii−i−ii−ii0000i3−i3i3−i33−33−3000000000000
χ392-2-22-222-222-2-2-22-222-2-22-2-22222-2-20000-2200000000000000000000000000002-200
χ402-2-22-222-222-2-2-22-222-2-22-2-22222-2-20000-220000000000000000000000000000-2200
χ412-2-22-222-222-2-2-22-22-222-2-2-222-2-22200002-2000000002-2002-2-220000000000000000
χ422-2-22-222-222-2-2-22-22-222-2-2-222-2-22200002-200000000-2200-222-20000000000000000
χ432-2-22-22-1-222-211-11-1-222-211-1-111-1-10000-11−i3i3i3−i3i3−i3−i3i32-200-111-1−i3i3i3−i3000000000000
χ442-2-22-22-1-222-211-11-1-222-211-1-111-1-10000-11−i3i3i3−i3i3−i3−i3i3-22001-1-11i3−i3−i3i3000000000000
χ452-2-22-22-1-222-211-11-1-222-211-1-111-1-10000-11i3−i3−i3i3−i3i3i3−i32-200-111-1i3−i3−i3i3000000000000
χ462-2-22-22-1-222-211-11-1-222-211-1-111-1-10000-11i3−i3−i3i3−i3i3i3−i3-22001-1-11−i3i3i3−i3000000000000
χ47444444-24444-2-2-2-2-2-4-4-4-4-2-2-2-2222200002200000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-2-2-2000022220000−2i2−2i22i22i200i2i2i2i2−i2−i2−i2−i2000000000000000000000000
χ49444444-2-4-4-4-4-2-2-2-2-20000222200002i22i2−2i2−2i200−i2−i2−i2−i2i2i2i2i2000000000000000000000000
χ504444-4-44-44-44444-4-40000-44-44000000000000000000000000000000000000000000
χ514444-4-4-24-44-4-2-2-2224-44-4-22-22-2-2-2-200002200000000000000000000000000000000
χ524444-4-4-2-44-44-2-2-22200002-22-20000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ534444-4-4-2-44-44-2-2-22200002-22-20000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ544-4-444-4-244-4-422-2-220000-222-2000022−2222−2200−22−22−22−22000000000000000000000000
χ554-4-444-4-244-4-422-2-220000-222-20000−2222−2222002−22−22−22−2000000000000000000000000
χ564-4-444-4-2-4-44422-2-22-4-4442-2-2222-2-200002-200000000000000000000000000000000
χ574-4-44-4444-4-44-4-44-44000044-4-4000000000000000000000000000000000000000000
χ584-4-44-44-24-4-4422-22-20000-2-22200000000006−6−666−6−66000000000000000000000000
χ594-4-44-44-24-4-4422-22-20000-2-2220000000000−666−6−666−6000000000000000000000000
χ604-4-44-44-2-444-422-22-24-4-4422-2-2-2-22200002-200000000000000000000000000000000
χ6188-8-800800008-8-80000000000000000000000000000000000000000000000000000
χ6288-8-800-40000-44400000000002i6−2i62i6−2i600000000000000000000000000000000000000
χ6388-8-800-40000-4440000000000−2i62i6−2i62i600000000000000000000000000000000000000
χ648-88-80080000-88-80000000000000000000000000000000000000000000000000000
χ658-88-800-400004-4400000000002i6−2i6−2i62i600000000000000000000000000000000000000
χ668-88-800-400004-440000000000−2i62i62i6−2i600000000000000000000000000000000000000

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