Finite Group Databasebeta

← Group #10691200

Character table — Group #10691200

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1222223444466612121212224444446666661212121212124488888888121212121212121224242424242424242424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-11−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111-1−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ1722222222222222222222-2-222-2-2222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-22200000000-2-2-2-222220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-22-200000000-2-222-2-2220000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2200000000-2-22222-2-20000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-11111-1-11111-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-222-2-222-1-11111-1-11111-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1111122000000001111-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1111122000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ29222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-222i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000
χ30222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-1111111-22−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1-1-1-1-11111112-20000000011-1-111-1-133−3−3−3−33333−3−3−3−333000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-2-2-222-1-1-1-1-1-11111112-20000000011-1-111-1-1−3−33333−3−3−3−33333−3−3000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1111111-1-1-1-12-22i2i−2i−2i−2i−2i2i2i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-22222-2-2-1-1111111-1-1-1-12-2−2i−2i2i2i2i2i−2i−2i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-220000000011-1-1-1-11133−3−3−3−333−3−33333−3−3000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-220000000011-1-1-1-111−3−33333−3−333−3−3−3−333000000000000
χ372222-2-2222-2-2222-2-2-2-2002-2002-2-2-200002200000000002i−2i2i−2i2-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000
χ382222-2-2222-2-2222-2-2-2-2002-2002-2-2-20000220000000000−2i2i−2i2i2-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ392222-2-2222-2-2222-2-2-2-200-2200-22-2-20000220000002i−2i2i−2i0000-22-2200002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ402222-2-2222-2-2222-2-2-2-200-2200-22-2-2000022000000−2i2i−2i2i0000-22-220000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ412222-2-22-2-2222222222002-200-22-2-20000-2-200000000002-2-222-2-220000000000002-22-2-22-22000000000000
χ422222-2-22-2-2222222222002-200-22-2-20000-2-20000000000-222-22-2-22000000000000-22-222-22-2000000000000
χ432222-2-22-2-222222222200-22002-2-2-20000-2-20000002-2-220000-222-200002-22-2-22-2200000000000000000000
χ442222-2-22-2-222222222200-22002-2-2-20000-2-2000000-222-20000-222-20000-22-222-22-200000000000000000000
χ452222-2-2-122-2-2-1-1-11111002-2002-211−i3−i3i3i3-1-1−i3−i3i3i30000002i−2i2i−2i-11-11−i3i3−i3i33−3−333−3−33−ii−ii−ii−ii000000000000
χ462222-2-2-122-2-2-1-1-11111002-2002-211−i3−i3i3i3-1-1−i3−i3i3i3000000−2i2i−2i2i-11-11−i3i3−i3i3−333−3−333−3i−ii−ii−ii−i000000000000
χ472222-2-2-122-2-2-1-1-11111002-2002-211i3i3−i3−i3-1-1i3i3−i3−i30000002i−2i2i−2i-11-11i3−i3i3−i3−333−3−333−3−ii−ii−ii−ii000000000000
χ482222-2-2-122-2-2-1-1-11111002-2002-211i3i3−i3−i3-1-1i3i3−i3−i3000000−2i2i−2i2i-11-11i3−i3i3−i33−3−333−3−33i−ii−ii−ii−i000000000000
χ492222-2-2-122-2-2-1-1-1111100-2200-2211−i3−i3i3i3-1-1−i3−i3i3i3002i−2i2i−2i00001-11-1i3−i3i3−i3−ii−ii−ii−ii3−3−333−3−33000000000000
χ502222-2-2-122-2-2-1-1-1111100-2200-2211−i3−i3i3i3-1-1−i3−i3i3i300−2i2i−2i2i00001-11-1i3−i3i3−i3i−ii−ii−ii−i−333−3−333−3000000000000
χ512222-2-2-122-2-2-1-1-1111100-2200-2211i3i3−i3−i3-1-1i3i3−i3−i3002i−2i2i−2i00001-11-1−i3i3−i3i3−ii−ii−ii−ii−333−3−333−3000000000000
χ522222-2-2-122-2-2-1-1-1111100-2200-2211i3i3−i3−i3-1-1i3i3−i3−i300−2i2i−2i2i00001-11-1−i3i3−i3i3i−ii−ii−ii−i3−3−333−3−33000000000000
χ532222-2-2-1-2-222-1-1-1-1-1-1-1002-200-2211−i3−i3i3i311i3i3−i3−i30000002-2-22-111-1−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-11-111-11-1000000000000
χ542222-2-2-1-2-222-1-1-1-1-1-1-1002-200-2211−i3−i3i3i311i3i3−i3−i3000000-222-2-111-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i31-11-1-11-11000000000000
χ552222-2-2-1-2-222-1-1-1-1-1-1-1002-200-2211i3i3−i3−i311−i3−i3i3i30000002-2-22-111-1i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-11-111-11-1000000000000
χ562222-2-2-1-2-222-1-1-1-1-1-1-1002-200-2211i3i3−i3−i311−i3−i3i3i3000000-222-2-111-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i31-11-1-11-11000000000000
χ572222-2-2-1-2-222-1-1-1-1-1-1-100-22002-211−i3−i3i3i311i3i3−i3−i3002-2-2200001-1-11i3−i3−i3i3-11-111-11-1−i3i3i3−i3i3−i3−i3i3000000000000
χ582222-2-2-1-2-222-1-1-1-1-1-1-100-22002-211−i3−i3i3i311i3i3−i3−i300-222-200001-1-11i3−i3−i3i31-11-1-11-11i3−i3−i3i3−i3i3i3−i3000000000000
χ592222-2-2-1-2-222-1-1-1-1-1-1-100-22002-211i3i3−i3−i311−i3−i3i3i3002-2-2200001-1-11−i3i3i3−i3-11-111-11-1i3−i3−i3i3−i3i3i3−i3000000000000
χ602222-2-2-1-2-222-1-1-1-1-1-1-100-22002-211i3i3−i3−i311−i3−i3i3i300-222-200001-1-11−i3i3i3−i31-11-1-11-11−i3i3i3−i3i3−i3−i3i3000000000000
χ6122-2-22-222-22-22-2-222-2-22-2002-2002-22-22-22-22-22-200000000000000000000000000000000002−22−22−22−20000
χ6222-2-22-222-22-22-2-222-2-22-2002-2002-22-22-22-22-22-20000000000000000000000000000000000−22−22−22−220000
χ6322-2-22-222-22-22-2-222-2-2-2200-22002-2-22-222-2-22-2200000000000000000000000000000000002−22−2−22−220000
χ6422-2-22-222-22-22-2-222-2-2-2200-22002-2-22-222-2-22-220000000000000000000000000000000000−22−222−22−20000
χ6522-2-22-22-22-222-2-2-2-2222-200-22002-22-22-2-22-22-220000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ6622-2-22-22-22-222-2-2-2-2222-200-22002-22-22-2-22-22-220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ6722-2-22-22-22-222-2-2-2-222-22002-2002-2-22-22-222-22-20000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ6822-2-22-22-22-222-2-2-2-222-22002-2002-2-22-22-222-22-20000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ6944-4-44-4-24-44-4-222-2-2224-4004-400-22-22-22-22-22-220000000000000000000000000000000000000000000000
χ7044-4-44-4-24-44-4-222-2-222-4400-4400-222-22-2-222-22-20000000000000000000000000000000000000000000000
χ7144-4-44-4-2-44-44-22222-2-24-400-4400-22-22-222-22-22-20000000000000000000000000000000000000000000000
χ7244-4-44-4-2-44-44-22222-2-2-44004-400-222-22-22-2-22-220000000000000000000000000000000000000000000000
χ7344-4-4-4444-4-444-4-4-4-44400000000-4400004-400000000000000000000000000000000000000000000000000
χ7444-4-4-444-444-44-4-444-4-400000000-440000-4400000000000000000000000000000000000000000000000000
χ7544-4-4-44-24-4-44-22222-2-2000000002-2−2i32i32i3−2i3-22−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7644-4-4-44-24-4-44-22222-2-2000000002-22i3−2i3−2i32i3-222i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ7744-4-4-44-2-444-4-222-2-222000000002-2−2i32i32i3−2i32-22i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ7844-4-4-44-2-444-4-222-2-222000000002-22i3−2i3−2i32i32-2−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ798-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000000000000000

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