Finite Group Databasebeta

← Group #10691055

Character table — Group #10691055

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
χ91111-1-111-1-1-11-1-1-1-1-111111-1ii−i−i1111-1-1-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-1-11ii−i−iii−i−i1-1
χ101111-1-111-1-1-11-1-1-1-1-111111-1ii−i−i1111-1-1-1-1ii−i−ii−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-11-1−i−iii−i−iii-11
χ111111-1-111-1-1-11-1-1-1-1-111111-1ii−i−i1111-1-1-1-1−i−iiii−i1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-111-11ii−i−i−i−iii-11
χ121111-1-111-1-1-11-1-1-1-1-111111-1ii−i−i1111-1-1-1-1−i−iiii−i1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-1111-1−i−iiiii−i−i1-1
χ131111-1-111-1-1-11-1-1-1-1-111111-1−i−iii1111-1-1-1-1ii−i−i−ii1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-111-11−i−iiiii−i−i-11
χ141111-1-111-1-1-11-1-1-1-1-111111-1−i−iii1111-1-1-1-1ii−i−i−ii1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-1111-1ii−i−i−i−iii1-1
χ151111-1-111-1-1-11-1-1-1-1-111111-1−i−iii1111-1-1-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-1-11−i−iii−i−iii1-1
χ161111-1-111-1-1-11-1-1-1-1-111111-1−i−iii1111-1-1-1-1−i−iii−ii1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-11-1ii−i−iii−i−i-11
χ17222222222-2-2222222222-2-2-2000022-2-22-22-2000000-2-200000000000000002222000000-2-20000000000
χ18222222222-2-2222222222-2-2-2000022-2-22-22-2000000-2-20000000000000000-2-2-2-2000000220000000000
χ192222222-2-222-2-222222222-2-20000-2-222-22-22000000-2-200000000000000000000000000002i−2i2i−2i000000
χ202222222-2-222-2-222222222-2-20000-2-222-22-22000000-2-20000000000000000000000000000−2i2i−2i2i000000
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
χ312222-2-222-2222-2-2-2-2-2222-2-22000022-2-2-22-22000000-22000000000000000022-2-20000002-20000000000
χ322222-2-222-2222-2-2-2-2-2222-2-22000022-2-2-22-22000000-220000000000000000-2-222000000-220000000000
χ332222-2-22-2222-22-2-2-2-2222-22-22222-2-2-2-222220000-2-22-222-2-2-2-222000000000000000000000000000000
χ342222-2-22-2222-22-2-2-2-2222-22-2-2-2-2-2-2-2-2-222220000222-2-2-22222-2-2000000000000000000000000000000
χ352222-2-22-22-2-2-22-2-2-2-22222-220000-2-2222-22-2000000-2200000000000000000000000000002-2-22000000
χ362222-2-22-22-2-2-22-2-2-2-22222-220000-2-2222-22-2000000-220000000000000000000000000000-222-2000000
χ372222-2-2-12-2-2-22-21111-1-1-122-22i2i−2i−2i-1-1-1-111112i2i−2i−2i2i−2i-11−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ382222-2-2-12-2-2-22-21111-1-1-122-22i2i−2i−2i-1-1-1-11111−2i−2i2i2i2i−2i-11−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ392222-2-2-12-2-2-22-21111-1-1-122-2−2i−2i2i2i-1-1-1-111112i2i−2i−2i−2i2i-11iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ402222-2-2-12-2-2-22-21111-1-1-122-2−2i−2i2i2i-1-1-1-11111−2i−2i2i2i−2i2i-11iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ412222-2-2-1-2222-221111-1-1-1-22-222221111-1-1-1-10000-2-2-11-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ422222-2-2-1-2222-221111-1-1-1-22-222221111-1-1-1-10000-2-2-11-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ432222-2-2-1-2222-221111-1-1-1-22-2-2-2-2-21111-1-1-1-1000022-1111-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ442222-2-2-1-2222-221111-1-1-1-22-2-2-2-2-21111-1-1-1-1000022-1111-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ4522-2-22-222200-2-222-2-22-2-200000002-20020-202−22−20000000000002−22−22−22−22-22-20000000000002−22−200
χ4622-2-22-222200-2-222-2-22-2-200000002-20020-202−22−20000000000002−22−22−22−2-22-22000000000000−22−2200
χ4722-2-22-222200-2-222-2-22-2-200000002-20020-20−22−22000000000000−22−22−22−222-22-2000000000000−22−2200
χ4822-2-22-222200-2-222-2-22-2-200000002-20020-20−22−22000000000000−22−22−22−22-22-220000000000002−22−200
χ4922-2-2-2222-200-22-2-2222-2-200000002-200-2020−i2i2i2−i2000000000000−i2i2−i2i2i2−i2i2−i22-2-22000000000000−i2i2i2−i200
χ5022-2-2-2222-200-22-2-2222-2-200000002-200-2020−i2i2i2−i2000000000000−i2i2−i2i2i2−i2i2−i2-222-2000000000000i2−i2−i2i200
χ5122-2-2-2222-200-22-2-2222-2-200000002-200-2020i2−i2−i2i2000000000000i2−i2i2−i2−i2i2−i2i22-2-22000000000000i2−i2−i2i200
χ5222-2-2-2222-200-22-2-2222-2-200000002-200-2020i2−i2−i2i2000000000000i2−i2i2−i2−i2i2−i2i2-222-2000000000000−i2i2i2−i200
χ53444444-244-4-444-2-2-2-2-2-2-2-4-4-40000-2-222-22-220000002200000000000000000000000000000000000000
χ54444444-2-4-444-4-4-2-2-2-2-2-2-24-4-4000022-2-22-22-20000002200000000000000000000000000000000000000
χ554444-4-4-24-4444-42222-2-2-2-4-440000-2-2222-22-20000002-200000000000000000000000000000000000000
χ564444-4-4-2-44-4-4-442222-2-2-24-44000022-2-2-22-220000002-200000000000000000000000000000000000000
χ5744-4-44-44-4-4004444-4-44-4-40000000-4400-40400000000000000000000000000000000000000000000000
χ5844-4-44-4-24400-4-4-2-222-2220000000-2200-202022−2222−22000000000000−22−22−22−220000000000000000000000
χ5944-4-44-4-24400-4-4-2-222-2220000000-2200-2020−2222−22220000000000002−22−22−22−20000000000000000000000
χ6044-4-44-4-2-4-40044-2-222-22200000002-20020-2000000000000000006−6−666−6−660000000000000000000000
χ6144-4-44-4-2-4-40044-2-222-22200000002-20020-200000000000000000−666−6−666−60000000000000000000000
χ6244-4-4-444-44004-4-4-4444-4-40000000-440040-400000000000000000000000000000000000000000000000
χ6344-4-4-44-24-400-4422-2-2-2220000000-220020-20−2i22i22i2−2i2000000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ6444-4-4-44-24-400-4422-2-2-2220000000-220020-202i2−2i2−2i22i2000000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ6544-4-4-44-2-44004-422-2-2-22200000002-200-20200000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ6644-4-4-44-2-44004-422-2-2-22200000002-200-20200000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ674-44-4004004-4000000-44-400022−2222−220000040-40000000022−22000022−22000000000000000000000000000000
χ684-44-4004004-4000000-44-4000−2222−22220000040-400000000−22220000−2222000000000000000000000000000000
χ694-44-400400-44000000-44-4000−2i22i22i2−2i200000-40400000000−2i22i200002i2−2i2000000000000000000000000000000
χ704-44-400400-44000000-44-40002i2−2i2−2i22i200000-404000000002i2−2i20000−2i22i2000000000000000000000000000000
χ714-44-400-2004-400−2i32i3−2i32i32-2200022−2222−2200−2i32i30-20200000000−22i6−i6i6−i6−22000000000000000000000000000000
χ724-44-400-2004-400−2i32i3−2i32i32-22000−2222−222200−2i32i30-202000000002−2−i6i6−i6i62−2000000000000000000000000000000
χ734-44-400-2004-4002i3−2i32i3−2i32-2200022−2222−22002i3−2i30-20200000000−22−i6i6−i6i6−22000000000000000000000000000000
χ744-44-400-2004-4002i3−2i32i3−2i32-22000−2222−2222002i3−2i30-202000000002−2i6−i6i6−i62−2000000000000000000000000000000
χ754-44-400-200-4400−2i32i3−2i32i32-22000−2i22i22i2−2i2002i3−2i3020-200000000i2−i2−666−6−i2i2000000000000000000000000000000
χ764-44-400-200-4400−2i32i3−2i32i32-220002i2−2i2−2i22i2002i3−2i3020-200000000−i2i26−6−66i2−i2000000000000000000000000000000
χ774-44-400-200-44002i3−2i32i3−2i32-22000−2i22i22i2−2i200−2i32i3020-200000000i2−i26−6−66−i2i2000000000000000000000000000000
χ784-44-400-200-44002i3−2i32i3−2i32-220002i2−2i2−2i22i200−2i32i3020-200000000−i2i2−666−6i2−i2000000000000000000000000000000
χ798-8-880080000000000-8-880000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-4000000−4i34i34i3−4i344-40000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-40000004i3−4i3−4i34i344-40000000000000000000000000000000000000000000000000000000000000

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