Finite Group Databasebeta

← Group #10692596

Character table — Group #10692596

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446661212121244466121212121212444488881212121212121212121224242424242424248824242424444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−ii−iii−i−i1-11-1ii−i−i1-1i−i
χ101111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−ii−iii−i−i-11-11−i−iii-11−ii
χ111111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−ii−i−iii1-11-1−i−iii1-1−ii
χ121111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-111-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−ii−i−iii-11-11ii−i−i-11i−i
χ131111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−ii−i−iii1-11-1ii−i−i-11−ii
χ141111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−ii−i−iii-11-11−i−iii1-1i−i
χ151111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiii−iii−i−i1-11-1−i−iii-11i−i
χ161111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiii−iii−i−i-11-11ii−i−i1-1−ii
χ172222222222-2-222222222-2-2-222-2-222-2-200000000-2-2000000000000000000000022-2-200000000
χ182222222222-2-222222222-2-2-222-2-222-2-200000000-2-20000000000000000000000-2-22200000000
χ192222222-2-2-222-2222-2-2-2-22-2-222-2-2-2-22200000000-2200000000000000000000002-2-2200000000
χ202222222-2-2-222-2222-2-2-2-22-2-222-2-2-2-22200000000-220000000000000000000000-222-200000000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ25222222-1-2-2-2-2-2-2-1-1-11111-222-1-1-1-1111122-2-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii2i−2i−i−iii000000000000
χ26222222-1-2-2-2-2-2-2-1-1-11111-222-1-1-1-1111122-2-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i−2i2iii−i−i000000000000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-1-1-11111-2-2222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii−2i2iii−i−i000000000000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-1-1-11111-2-222−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i2i−2i−i−iii000000000000
χ292222-2-222-2222-22222222-22-2-2-222-2-22200000000-2-2000000000000000000000000002-22-20000
χ302222-2-222-2222-22222222-22-2-2-222-2-22200000000-2-200000000000000000000000000-22-220000
χ312222-2-222-22-2-2-222222222-22-2-2-2-2-2-2-2-200002i−2i2i−2i22000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ322222-2-222-22-2-2-222222222-22-2-2-2-2-2-2-2-20000−2i2i−2i2i2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ332222-2-22-22-2222222-2-2-2-2-2-22-2-2-2-2222200002-2-222-20000000022-2-2-2-222000000000000000000
χ342222-2-22-22-2222222-2-2-2-2-2-22-2-2-2-222220000-222-22-200000000-2-22222-2-2000000000000000000
χ352222-2-22-22-2-2-22222-2-2-2-222-2-2-22222-2-200000000-22000000000000000000000000002i−2i−2i2i0000
χ362222-2-22-22-2-2-22222-2-2-2-222-2-2-22222-2-200000000-2200000000000000000000000000−2i2i2i−2i0000
χ372222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-221111111100002i−2i2i−2i-1-133−3−333−3−3−i−iii−i−iii00−i3i3−i3i3000000000000
χ382222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-221111111100002i−2i2i−2i-1-1−3−333−3−333−i−iii−i−iii00i3−i3i3−i3000000000000
χ392222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-22111111110000−2i2i−2i2i-1-133−3−333−3−3ii−i−iii−i−i00i3−i3i3−i3000000000000
χ402222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-22111111110000−2i2i−2i2i-1-1−3−333−3−333ii−i−iii−i−i00−i3i3−i3i3000000000000
χ412222-2-2-1-22-2222-1-1-11111-2-221111-1-1-1-100002-2-22-1133−3−3−3−333-1-11111-1-100−333−3000000000000
χ422222-2-2-1-22-2222-1-1-11111-2-221111-1-1-1-100002-2-22-11−3−33333−3−3-1-11111-1-1003−3−33000000000000
χ432222-2-2-1-22-2222-1-1-11111-2-221111-1-1-1-10000-222-2-1133−3−3−3−33311-1-1-1-111003−3−33000000000000
χ442222-2-2-1-22-2222-1-1-11111-2-221111-1-1-1-10000-222-2-11−3−33333−3−311-1-1-1-11100−333−3000000000000
χ45444444-2444-4-44-2-2-2-2-2-2-2-4-4-4-2-222-2-22200000000220000000000000000000000000000000000
χ46444444-2-4-4-444-4-2-2-222224-4-4-2-22222-2-2000000002-20000000000000000000000000000000000
χ474444-4-4-24-4444-4-2-2-2-2-2-2-2-44-422-2-222-2-200000000220000000000000000000000000000000000
χ484444-4-4-2-44-4-4-44-2-2-2222244-422-2-2-2-222000000002-20000000000000000000000000000000000
χ4944-4-40040004-404-4-400000000000004-42-22-20000002-22-22-22-200000000000000000000000000
χ5044-4-40040004-404-4-400000000000004-4-22-22000000-22-22-22-2200000000000000000000000000
χ5144-4-4004000-4404-4-40000000000000-442-2-220000002-22-2-22-2200000000000000000000000000
χ5244-4-4004000-4404-4-40000000000000-44-222-2000000-22-222-22-200000000000000000000000000
χ5344-4-400-20004-40-22223−2323−230000023−2300-222-22-2000000−1+31−3−1−31+3−1−31+3−1+31−300000000000000000000000000
χ5444-4-400-20004-40-22223−2323−230000023−2300-22-22-220000001−3−1+31+3−1−31+3−1−31−3−1+300000000000000000000000000
χ5544-4-400-20004-40-222−2323−232300000−232300-222-22-2000000−1−31+3−1+31−3−1+31−3−1−31+300000000000000000000000000
χ5644-4-400-20004-40-222−2323−232300000−232300-22-22-220000001+3−1−31−3−1+31−3−1+31+3−1−300000000000000000000000000
χ5744-4-400-2000-440-22223−2323−2300000−2323002-22-2-22000000−1−31+3−1+31−31−3−1+31+3−1−300000000000000000000000000
χ5844-4-400-2000-440-22223−2323−2300000−2323002-2-222-20000001+3−1−31−3−1+3−1+31−3−1−31+300000000000000000000000000
χ5944-4-400-2000-440-222−2323−23230000023−23002-22-2-22000000−1+31−3−1−31+31+3−1−31−3−1+300000000000000000000000000
χ6044-4-400-2000-440-222−2323−23230000023−23002-2-222-20000001−3−1+31+3−1−3−1−31+3−1+31−300000000000000000000000000
χ614-4-444-4444-400-4-44-444-4-40004-4004-40000000000000000000000000000000000000000000000
χ624-4-444-44-4-44004-44-4-4-4440004-400-440000000000000000000000000000000000000000000000
χ634-4-444-4-244-400-42-22-2-222000-2200-2200000000000000000000i6−i6i6−i6i6−i6i6−i6000000000000000000
χ644-4-444-4-244-400-42-22-2-222000-2200-2200000000000000000000−i6i6−i6i6−i6i6−i6i6000000000000000000
χ654-4-444-4-2-4-440042-2222-2-2000-22002-2000000000000000000006−66−6−66−66000000000000000000
χ664-4-444-4-2-4-440042-2222-2-2000-22002-200000000000000000000−66−666−66−6000000000000000000
χ674-4-44-4444-4-4004-44-444-4-4000-4400-440000000000000000000000000000000000000000000000
χ684-4-44-444-44400-4-44-4-4-444000-44004-40000000000000000000000000000000000000000000000
χ694-4-44-44-24-4-40042-22-2-2220002-2002-2000000000000000000006−6−666−6−66000000000000000000
χ704-4-44-44-24-4-40042-22-2-2220002-2002-200000000000000000000−666−6−666−6000000000000000000
χ714-4-44-44-2-44400-42-2222-2-20002-200-2200000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000
χ724-4-44-44-2-44400-42-2222-2-20002-200-2200000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000
χ738-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000
χ758-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000

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