Finite Group Databasebeta

← Group #10691069

Character table — Group #10691069

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order122222344444466666664448888121212121212121288888812122424242424242424242424242424242422444412121212448888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ91111-1-11-11-1-11-1-1-1-1-111111-1ii−i−i11-111-1-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-11-1ii−i−iii−i−i1-1
χ101111-1-11-11-1-11-1-1-1-1-111111-1ii−i−i11-111-1-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-1-11−i−iii−i−iii-11
χ111111-1-11-11-1-11-1-1-1-1-111111-1ii−i−i11-111-1-1-1−i−iiii−i1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-1111-1ii−i−i−i−iii-11
χ121111-1-11-11-1-11-1-1-1-1-111111-1ii−i−i11-111-1-1-1−i−iiii−i1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-111-11−i−iiiii−i−i1-1
χ131111-1-11-11-1-11-1-1-1-1-111111-1−i−iii11-111-1-1-1ii−i−i−ii1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-1111-1−i−iiiii−i−i-11
χ141111-1-11-11-1-11-1-1-1-1-111111-1−i−iii11-111-1-1-1ii−i−i−ii1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-111-11ii−i−i−i−iii1-1
χ151111-1-11-11-1-11-1-1-1-1-111111-1−i−iii11-111-1-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-11-1−i−iii−i−iii1-1
χ161111-1-11-11-1-11-1-1-1-1-111111-1−i−iii11-111-1-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-1-11ii−i−iii−i−i-11
χ1722222222-2-22-2-222222222-2-20000222-2-2-22-2000000-2-200000000000000000000000000002i−2i2i−2i000000
χ1822222222-2-22-2-222222222-2-20000222-2-2-22-2000000-2-20000000000000000000000000000−2i2i−2i2i000000
χ192222222-222-2222222222-2-2-20000-2-2-2222-22000000-2-200000000000000002222000000-2-20000000000
χ202222222-222-2222222222-2-2-20000-2-2-2222-22000000-2-20000000000000000-2-2-2-2000000220000000000
χ212222222-2-2-2-2-2-22222222-2222i2i−2i−2i-2-2-2-2-2-2-2-20000−2i2i222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000
χ222222222-2-2-2-2-2-22222222-222−2i−2i2i2i-2-2-2-2-2-2-2-200002i−2i22−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000
χ23222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2222i2i−2i−2i111111110000−2i2i-1-1−i−iii−i−iii33−3−333−3−3000000−i3i3−i3i3000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2222i2i−2i−2i111111110000−2i2i-1-1−i−iii−i−iii−3−333−3−333000000i3−i3i3−i3000000000000
χ29222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222−2i−2i2i2i1111111100002i−2i-1-1ii−i−iii−i−i33−3−333−3−3000000i3−i3i3−i3000000000000
χ30222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222−2i−2i2i2i1111111100002i−2i-1-1ii−i−iii−i−i−3−333−3−333000000−i3i3−i3i3000000000000
χ312222-2-2222-222-2-2-2-2-2222-2-220000-2-2222-22-2000000-22000000000000000022-2-2000000-220000000000
χ322222-2-2222-222-2-2-2-2-2222-2-220000-2-2222-22-2000000-220000000000000000-2-2220000002-20000000000
χ332222-2-222-222-22-2-2-2-2222-22-22222-2-22-2-22220000-2-22-222-2-2-2-222000000000000000000000000000000
χ342222-2-222-222-22-2-2-2-2222-22-2-2-2-2-2-2-22-2-22220000222-2-2-22222-2-2000000000000000000000000000000
χ352222-2-22-2-22-2-22-2-2-2-22222-22000022-2-2-22-22000000-2200000000000000000000000000002-2-22000000
χ362222-2-22-2-22-2-22-2-2-2-22222-22000022-2-2-22-22000000-220000000000000000000000000000-222-2000000
χ372222-2-2-12-222-221111-1-1-1-22-2222211-111-1-1-10000-2-2-11-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ382222-2-2-12-222-221111-1-1-1-22-2222211-111-1-1-10000-2-2-11-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ392222-2-2-12-222-221111-1-1-1-22-2-2-2-2-211-111-1-1-1000022-1111-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ402222-2-2-12-222-221111-1-1-1-22-2-2-2-2-211-111-1-1-1000022-1111-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ412222-2-2-1-22-2-22-21111-1-1-122-22i2i−2i−2i-1-11-1-11112i2i−2i−2i2i−2i-11−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ422222-2-2-1-22-2-22-21111-1-1-122-22i2i−2i−2i-1-11-1-1111−2i−2i2i2i2i−2i-11−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ432222-2-2-1-22-2-22-21111-1-1-122-2−2i−2i2i2i-1-11-1-11112i2i−2i−2i−2i2i-11iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ442222-2-2-1-22-2-22-21111-1-1-122-2−2i−2i2i2i-1-11-1-1111−2i−2i2i2i−2i2i-11iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ452-2-222-220-2202-222-2-2-2-2200000000002-220-2−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i22-22-2000000000000−i2i2−i2i200
χ462-2-222-220-2202-222-2-2-2-2200000000002-220-2−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i2-22-22000000000000i2−i2i2−i200
χ472-2-222-220-2202-222-2-2-2-2200000000002-220-2i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i22-22-2000000000000i2−i2i2−i200
χ482-2-222-220-2202-222-2-2-2-2200000000002-220-2i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i2-22-22000000000000−i2i2−i2i200
χ492-2-22-2220-2-2022-2-222-2-2200000000002-2-2022−2−220000000000002−22−2−22−222-2-220000000000002−2−2200
χ502-2-22-2220-2-2022-2-222-2-2200000000002-2-2022−2−220000000000002−22−2−22−22-222-2000000000000−222−200
χ512-2-22-2220-2-2022-2-222-2-2200000000002-2-202−222−2000000000000−22−222−22−22-2-22000000000000−222−200
χ522-2-22-2220-2-2022-2-222-2-2200000000002-2-202−222−2000000000000−22−222−22−2-222-20000000000002−2−2200
χ53444444-24-4-44-4-4-2-2-2-2-2-2-24-4-40000-2-2-2222-220000002200000000000000000000000000000000000000
χ54444444-2-444-444-2-2-2-2-2-2-2-4-4-40000222-2-2-22-20000002200000000000000000000000000000000000000
χ554444-4-4-244-444-42222-2-2-2-4-44000022-2-2-22-220000002-200000000000000000000000000000000000000
χ564444-4-4-2-4-44-4-442222-2-2-24-440000-2-2222-22-20000002-200000000000000000000000000000000000000
χ5744-4-4004400-40000004-4-400022−2222−22004000-400000000022−22000022−22000000000000000000000000000000
χ5844-4-4004400-40000004-4-4000−2222−2222004000-4000000000−22220000−2222000000000000000000000000000000
χ5944-4-4004-40040000004-4-4000−2i22i22i2−2i200-40004000000000−2i22i200002i2−2i2000000000000000000000000000000
χ6044-4-4004-40040000004-4-40002i2−2i2−2i22i200-400040000000002i2−2i20000−2i22i2000000000000000000000000000000
χ6144-4-400-2400-400−2i32i3−2i32i3-22200022−2222−22−2i32i3-20002000000000−22i6−i6i6−i6−22000000000000000000000000000000
χ6244-4-400-2400-400−2i32i3−2i32i3-222000−2222−2222−2i32i3-200020000000002−2−i6i6−i6i62−2000000000000000000000000000000
χ6344-4-400-2400-4002i3−2i32i3−2i3-22200022−2222−222i3−2i3-20002000000000−22−i6i6−i6i6−22000000000000000000000000000000
χ6444-4-400-2400-4002i3−2i32i3−2i3-222000−2222−22222i3−2i3-200020000000002−2i6−i6i6−i62−2000000000000000000000000000000
χ6544-4-400-2-400400−2i32i3−2i32i3-222000−2i22i22i2−2i22i3−2i32000-2000000000i2−i2−666−6−i2i2000000000000000000000000000000
χ6644-4-400-2-400400−2i32i3−2i32i3-2220002i2−2i2−2i22i22i3−2i32000-2000000000−i2i26−6−66i2−i2000000000000000000000000000000
χ6744-4-400-2-4004002i3−2i32i3−2i3-222000−2i22i22i2−2i2−2i32i32000-2000000000i2−i26−6−66−i2i2000000000000000000000000000000
χ6844-4-400-2-4004002i3−2i32i3−2i3-2220002i2−2i2−2i22i2−2i32i32000-2000000000−i2i2−666−6i2−i2000000000000000000000000000000
χ694-4-444-4404-40-4444-4-4-4-440000000000-44-4040000000000000000000000000000000000000000000000
χ704-4-444-4-204-40-44-2-22222-200000000002-220-20000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ714-4-444-4-204-40-44-2-22222-200000000002-220-20000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ724-4-444-4-20-4404-4-2-22222-20000000000-22-202−2i22i2−2i22i2000000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ734-4-444-4-20-4404-4-2-22222-20000000000-22-2022i2−2i22i2−2i2000000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ744-4-44-4440440-4-4-4-444-4-440000000000-4440-40000000000000000000000000000000000000000000000
χ754-4-44-44-20440-4-422-2-222-200000000002-2-20200000000000000006−6−66−666−60000000000000000000000
χ764-4-44-44-20440-4-422-2-222-200000000002-2-2020000000000000000−666−66−6−660000000000000000000000
χ774-4-44-44-20-4-404422-2-222-20000000000-2220-222−22−2222000000000000−22−222−22−20000000000000000000000
χ784-4-44-44-20-4-404422-2-222-20000000000-2220-2−222222−220000000000002−22−2−22−220000000000000000000000
χ798-88-80080000000000-88-80000000000000000000000000000000000000000000000000000000000000
χ808-88-800-4000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000

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