Finite Group Databasebeta

← Group #10691687

Character table — Group #10691687

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order122222344444466666664448888121212121212121288888812122424242424242424242424242424242488884412121212224488888888
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
χ511111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ611111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ91111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1ii−i−ii−i11iiii−i−i−i−iiiii−i−i−i−iii−i−i1-111-1-11-11-1i−i11-1-1i−i
χ101111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1ii−i−ii−i11iiii−i−i−i−iiiii−i−i−i−i−i−iii1-111-1-1-11-11−ii-1-111−ii
χ111111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1−i−iiii−i11iiii−i−i−i−i−i−i−i−iiiiiii−i−i-11-1-1111-11-1i−i-1-111−ii
χ121111111-1-1-1-1-1-11111111-111ii−i−i-1-1-1-1-1-1-1-1−i−iiii−i11iiii−i−i−i−i−i−i−i−iiiii−i−iii-11-1-111-11-11−ii11-1-1i−i
χ131111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1ii−i−i−ii11−i−i−i−iiiiiiiii−i−i−i−iii−i−i-11-1-111-11-11i−i11-1-1−ii
χ141111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1ii−i−i−ii11−i−i−i−iiiiiiiii−i−i−i−i−i−iii-11-1-1111-11-1−ii-1-111i−i
χ151111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1−i−iii−ii11−i−i−i−iiiii−i−i−i−iiiiiii−i−i1-111-1-1-11-11i−i-1-111i−i
χ161111111-1-1-1-1-1-11111111-111−i−iii-1-1-1-1-1-1-1-1−i−iii−ii11−i−i−i−iiiii−i−i−i−iiiii−i−iii1-111-1-11-11-1−ii11-1-1−ii
χ1722222222-22-2-2-222222222-2-20000222-2-2-22-2000000-2-200000000000000002i2i−2i−2i0000000000−2i2i000000
χ1822222222-22-2-2-222222222-2-20000222-2-2-22-2000000-2-20000000000000000−2i−2i2i2i00000000002i−2i000000
χ192222222-22-22222222222-2-2-20000-2-2-2222-22000000-2-2000000000000000022220000000000-2-2000000
χ202222222-22-22222222222-2-2-20000-2-2-2222-22000000-2-20000000000000000-2-2-2-2000000000022000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-12222-2-2-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ25222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2222i2i−2i−2i111111112i2i−2i−2i2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ26222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2222i2i−2i−2i11111111−2i−2i2i2i2i−2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ27222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222−2i−2i2i2i111111112i2i−2i−2i−2i2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ28222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-222−2i−2i2i2i11111111−2i−2i2i2i−2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ292222-2-22222-2-22-2-2-2-2222-2-2200002-2-222-22-20000002-20000000000000000000000000022-2-200000000
χ302222-2-22222-2-22-2-2-2-2222-2-2200002-2-222-22-20000002-200000000000000000000000000-2-22200000000
χ312222-2-222-2222-2-2-2-2-2222-22-222222-2-2-2-22220000-2-2-2222-2-222-2-2000000000000000000000000000000
χ322222-2-222-2222-2-2-2-2-2222-22-2-2-2-2-22-2-2-2-2222000022-22-2-222-2-222000000000000000000000000000000
χ332222-2-22-22-2-2-22-2-2-2-222222-22i2i−2i−2i-22222-2-2-20000−2i2i-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ342222-2-22-22-2-2-22-2-2-2-222222-2−2i−2i2i2i-22222-2-2-200002i−2i-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ352222-2-22-2-2-222-2-2-2-2-22222-220000-222-2-22-220000002-2000000000000000000000000002-2-2200000000
χ362222-2-22-2-2-222-2-2-2-2-22222-220000-222-2-22-220000002-200000000000000000000000000-222-200000000
χ372222-2-2-12-2222-21111-1-1-1-22-22222-11111-1-1-10000-2-21-1-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-12-2222-21111-1-1-1-22-22222-11111-1-1-10000-2-21-1-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-12-2222-21111-1-1-1-22-2-2-2-2-2-11111-1-1-10000221-111-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-12-2222-21111-1-1-1-22-2-2-2-2-2-11111-1-1-10000221-111-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-1-22-2-2-221111-1-1-122-22i2i−2i−2i1-1-1-1-11110000−2i2i1-1−i−iiiii−i−i33−3−3−3−333000000−i3i3i3−i3000000000000
χ422222-2-2-1-22-2-2-221111-1-1-122-22i2i−2i−2i1-1-1-1-11110000−2i2i1-1−i−iiiii−i−i−3−33333−3−3000000i3−i3−i3i3000000000000
χ432222-2-2-1-22-2-2-221111-1-1-122-2−2i−2i2i2i1-1-1-1-111100002i−2i1-1ii−i−i−i−iii33−3−3−3−333000000i3−i3−i3i3000000000000
χ442222-2-2-1-22-2-2-221111-1-1-122-2−2i−2i2i2i1-1-1-1-111100002i−2i1-1ii−i−i−i−iii−3−33333−3−3000000−i3i3i3−i3000000000000
χ452-2-222-22020-22-222-2-22-2-200000000002-2-202−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i22-22-2000000000000−i2i2−i2i200
χ462-2-222-22020-22-222-2-22-2-200000000002-2-202−i2i2−i2i2000000000000−i2i2−i2i2−i2i2−i2i2-22-22000000000000i2−i2i2−i200
χ472-2-222-22020-22-222-2-22-2-200000000002-2-202i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i22-22-2000000000000i2−i2i2−i200
χ482-2-222-22020-22-222-2-22-2-200000000002-2-202i2−i2i2−i2000000000000i2−i2i2−i2i2−i2i2−i2-22-22000000000000−i2i2−i2i200
χ492-2-222-220-202-2222-2-22-2-20000000000-2220-22−2−220000000000002−22−2−22−222i−2i−2i2i000000000000−i2i2i2−i200
χ502-2-222-220-202-2222-2-22-2-20000000000-2220-22−2−220000000000002−22−2−22−22−2i2i2i−2i000000000000i2−i2−i2i200
χ512-2-222-220-202-2222-2-22-2-20000000000-2220-2−222−2000000000000−22−222−22−22i−2i−2i2i000000000000i2−i2−i2i200
χ522-2-222-220-202-2222-2-22-2-20000000000-2220-2−222−2000000000000−22−222−22−2−2i2i2i−2i000000000000−i2i2i2−i200
χ53444444-24-44-4-4-4-2-2-2-2-2-2-24-4-40000-2-2-2222-220000002200000000000000000000000000000000000000
χ54444444-2-44-4444-2-2-2-2-2-2-2-4-4-40000222-2-2-22-20000002200000000000000000000000000000000000000
χ554444-4-4-2444-4-442222-2-2-2-4-440000-222-2-22-22000000-2200000000000000000000000000000000000000
χ564444-4-4-2-4-4-444-42222-2-2-24-4400002-2-222-22-2000000-2200000000000000000000000000000000000000
χ5744-4-400440-40000000-44-400022−2222−22400000-400000000022−220022−2200000000000000000000000000000000
χ5844-4-400440-40000000-44-4000−2222−2222400000-4000000000−222200−222200000000000000000000000000000000
χ5944-4-4004-4040000000-44-4000−2i22i22i2−2i2-4000004000000000−2i22i2002i2−2i200000000000000000000000000000000
χ6044-4-4004-4040000000-44-40002i2−2i2−2i22i2-40000040000000002i2−2i200−2i22i200000000000000000000000000000000
χ6144-4-400-240-4000−2i32i3−2i32i32-2200022−2222−22-2−2i32i30002000000000−22i6−i6−22i6−i6000000000000000000000000000000
χ6244-4-400-240-4000−2i32i3−2i32i32-22000−2222−2222-2−2i32i300020000000002−2−i6i62−2−i6i6000000000000000000000000000000
χ6344-4-400-240-40002i3−2i32i3−2i32-2200022−2222−22-22i3−2i30002000000000−22−i6i6−22−i6i6000000000000000000000000000000
χ6444-4-400-240-40002i3−2i32i3−2i32-22000−2222−2222-22i3−2i300020000000002−2i6−i62−2i6−i6000000000000000000000000000000
χ6544-4-400-2-404000−2i32i3−2i32i32-22000−2i22i22i2−2i222i3−2i3000-2000000000i2−i26−6−i2i2−66000000000000000000000000000000
χ6644-4-400-2-404000−2i32i3−2i32i32-220002i2−2i2−2i22i222i3−2i3000-2000000000−i2i2−66i2−i26−6000000000000000000000000000000
χ6744-4-400-2-4040002i3−2i32i3−2i32-22000−2i22i22i2−2i22−2i32i3000-2000000000i2−i2−66−i2i26−6000000000000000000000000000000
χ6844-4-400-2-4040002i3−2i32i3−2i32-220002i2−2i2−2i22i22−2i32i3000-2000000000−i2i26−6i2−i2−66000000000000000000000000000000
χ694-4-444-4-2040-44-4-2-222-2220000000000-2220-2−2i22i2−2i22i2000000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ704-4-444-4-2040-44-4-2-222-2220000000000-2220-22i2−2i22i2−2i2000000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ714-4-444-4-20-404-44-2-222-22200000000002-2-20222−22−2222000000000000−22−222−22−20000000000000000000000
χ724-4-444-4-20-404-44-2-222-22200000000002-2-202−222222−220000000000002−22−2−22−220000000000000000000000
χ734-4-44-4440404-4-4-4-4444-4-400000000004-440-40000000000000000000000000000000000000000000000
χ744-4-44-4440-40-444-4-4444-4-40000000000-44-4040000000000000000000000000000000000000000000000
χ754-4-44-44-20404-4-422-2-2-2220000000000-22-2020000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ764-4-44-44-20404-4-422-2-2-2220000000000-22-2020000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ774-4-44-44-20-40-44422-2-2-22200000000002-220-200000000000000006−6−666−6−660000000000000000000000
χ784-4-44-44-20-40-44422-2-2-22200000000002-220-20000000000000000−666−6−666−60000000000000000000000
χ798-88-80080000000000-8-880000000000000000000000000000000000000000000000000000000000000
χ808-88-800-4000000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000

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