Finite Group Databasebeta

← Group #10691065

Character table — Group #10691065

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446661212121244466888812121212121288888812122424242424242424242424242424242422448824242424448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ91111-1-11-11-11-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-11-1ii−i−iii−i−i1-1
χ101111-1-11-11-11-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-1-11−i−iii−i−iii-11
χ111111-1-11-11-11-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−i−i−iii11−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-1111-1−i−iiiii−i−i-11
χ121111-1-11-11-11-1-1111111111-1-1-1ii−i−i-1-1-1-1-1-1i−i−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-111-11ii−i−i−i−iii1-1
χ131111-1-11-11-11-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−iiii−i−i11iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-1111-1ii−i−i−i−iii-11
χ141111-1-11-11-11-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−iiii−i−i11iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-111-11−i−iiiii−i−i1-1
χ151111-1-11-11-11-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−ii−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-11-1−i−iii−i−iii1-1
χ161111-1-11-11-11-1-1111111111-1-1-1−i−iii-1-1-1-1-1-1−ii−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-1-11ii−i−iii−i−i-11
χ1722222222-2-2-22-2222-2-2-2-22-2-222000022-2-2-2-20000002-2000000000000000000000000000000002i−2i2i−2i00
χ1822222222-2-2-22-2222-2-2-2-22-2-222000022-2-2-2-20000002-200000000000000000000000000000000−2i2i−2i2i00
χ192222222-2222-222222222-2-2-2220000-2-22-2-22000000-2-200000000000000002222000000-2-20000000000
χ202222222-2222-222222222-2-2-2220000-2-22-2-22000000-2-20000000000000000-2-2-2-2000000220000000000
χ212222222-2-2-2-2-2-2222-2-2-2-2-222222i2i−2i−2i-2-2-222-2−2i2i0000-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-2-22222−2i−2i2i2i-2-2-222-22i−2i0000-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-12222-1-1-1-1-1-122-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-1000000000000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i111-1-11−2i2i00001-1−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii0000003−33−3000000000000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i111-1-11−2i2i00001-1i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii000000−33−33000000000000
χ29222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i111-1-112i−2i00001-1−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i000000−33−33000000000000
χ30222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i111-1-112i−2i00001-1i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i0000003−33−3000000000000
χ312222-2-2222-222-22222222-2-22-2-2000022-222-2000000-2-2000000000000000022-2-2000000-220000000000
χ322222-2-2222-222-22222222-2-22-2-2000022-222-2000000-2-20000000000000000-2-2220000002-20000000000
χ332222-2-222-22-222222-2-2-2-2-22-2-2-22222222-2-22-2-20000-220000000022-2-2-2-2220000000000000000000000
χ342222-2-222-22-222222-2-2-2-2-22-2-2-2-2-2-2-2222-2-22220000-2200000000-2-22222-2-20000000000000000000000
χ352222-2-22-2-22-2-22222-2-2-2-22-22-2-20000-2-222220000002-2000000000000000000000000000000002-2-2200
χ362222-2-22-2-22-2-22222-2-2-2-22-22-2-20000-2-222220000002-200000000000000000000000000000000-222-200
χ372222-2-2-12-22-222-1-1-11111-22-2112222-1-1-111-1-2-200001-133−3−3−3−333-1-11111-1-1000000−333−3000000000000
χ382222-2-2-12-22-222-1-1-11111-22-2112222-1-1-111-1-2-200001-1−3−33333−3−3-1-11111-1-10000003−3−33000000000000
χ392222-2-2-12-22-222-1-1-11111-22-211-2-2-2-2-1-1-111-12200001-133−3−3−3−33311-1-1-1-1110000003−3−33000000000000
χ402222-2-2-12-22-222-1-1-11111-22-211-2-2-2-2-1-1-111-12200001-1−3−33333−3−311-1-1-1-111000000−333−3000000000000
χ412222-2-2-1-22-22-2-2-1-1-1-1-1-1-122-2112i2i−2i−2i1111112i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-111000000000000
χ422222-2-2-1-22-22-2-2-1-1-1-1-1-1-122-2112i2i−2i−2i1111112i−2i−2i−2i2i2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-1000000000000
χ432222-2-2-1-22-22-2-2-1-1-1-1-1-1-122-211−2i−2i2i2i111111−2i2i2i2i−2i−2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-1000000000000
χ442222-2-2-1-22-22-2-2-1-1-1-1-1-1-122-211−2i−2i2i2i111111−2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-111000000000000
χ452-2-222-220-2220-22-2-2-2-2220002-2000000200-200−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000002-22-200000000−i2i2−i2i2000000
χ462-2-222-220-2220-22-2-2-2-2220002-2000000200-200−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200000000-22-2200000000i2−i2i2−i2000000
χ472-2-222-220-2220-22-2-2-2-2220002-2000000200-200i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000002-22-200000000i2−i2i2−i2000000
χ482-2-222-220-2220-22-2-2-2-2220002-2000000200-200i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200000000-22-2200000000−i2i2−i2i2000000
χ492-2-22-2220-2-22022-2-2-2-222000-22000000-2002002−2−22002−22−2−22−22000000002-2-22000000002−2−22000000
χ502-2-22-2220-2-22022-2-2-2-222000-22000000-2002002−2−22002−22−2−22−2200000000-222-200000000−222−2000000
χ512-2-22-2220-2-22022-2-2-2-222000-22000000-200200−222−200−22−222−22−2000000002-2-2200000000−222−2000000
χ522-2-22-2220-2-22022-2-2-2-222000-22000000-200200−222−200−22−222−22−200000000-222-2000000002−2−22000000
χ53444444-24-4-4-44-4-2-2-222224-4-4-2-20000-2-22222000000-2200000000000000000000000000000000000000
χ54444444-2-4444-44-2-2-2-2-2-2-2-4-4-4-2-2000022-222-20000002200000000000000000000000000000000000000
χ554444-4-4-244-444-4-2-2-2-2-2-2-2-4-44220000-2-22-2-220000002200000000000000000000000000000000000000
χ564444-4-4-2-4-44-4-44-2-2-222224-4422000022-2-2-2-2000000-2200000000000000000000000000000000000000
χ5744-4-40044000-40-44-400000000022−2222−224-40000000000000000000022−22000022−220000000000000000000000
χ5844-4-40044000-40-44-4000000000−2222−22224-400000000000000000000−22220000−22220000000000000000000000
χ5944-4-4004-400040-44-4000000000−2i22i22i2−2i2-4400000000000000000000−2i22i200002i2−2i20000000000000000000000
χ6044-4-4004-400040-44-40000000002i2−2i2−2i22i2-44000000000000000000002i2−2i20000−2i22i20000000000000000000000
χ6144-4-400-24000-402-2223−2323−230000022−2222−22-22023−2300000000000000000−226−66−6−220000000000000000000000
χ6244-4-400-24000-402-2223−2323−2300000−2222−2222-22023−23000000000000000002−2−66−662−20000000000000000000000
χ6344-4-400-24000-402-22−2323−23230000022−2222−22-220−232300000000000000000−22−66−66−220000000000000000000000
χ6444-4-400-24000-402-22−2323−232300000−2222−2222-220−2323000000000000000002−26−66−62−20000000000000000000000
χ6544-4-400-2-4000402-2223−2323−2300000−2i22i22i2−2i22-20−232300000000000000000i2−i2−i6i6i6−i6−i2i20000000000000000000000
χ6644-4-400-2-4000402-2223−2323−23000002i2−2i2−2i22i22-20−232300000000000000000−i2i2i6−i6−i6i6i2−i20000000000000000000000
χ6744-4-400-2-4000402-22−2323−232300000−2i22i22i2−2i22-2023−2300000000000000000i2−i2i6−i6−i6i6−i2i20000000000000000000000
χ6844-4-400-2-4000402-22−2323−2323000002i2−2i2−2i22i22-2023−2300000000000000000−i2i2−i6i6i6−i6i2−i20000000000000000000000
χ694-4-444-4404-4-4044-4-444-4-40004-4000000-40040000000000000000000000000000000000000000000000
χ704-4-444-4-204-4-404-222-2-222000-22000000200-2000000006−6−666−6−66000000000000000000000000000000
χ714-4-444-4-204-4-404-222-2-222000-22000000200-200000000−666−6−666−6000000000000000000000000000000
χ724-4-444-4-20-4440-4-22222-2-2000-22000000-200200−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ734-4-444-4-20-4440-4-22222-2-2000-22000000-2002002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ744-4-44-444044-40-44-4-444-4-4000-44000000400-40000000000000000000000000000000000000000000000
χ754-4-44-44-2044-40-4-222-2-2220002-2000000-200200000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000000000
χ764-4-44-44-2044-40-4-222-2-2220002-2000000-200200000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000000000
χ774-4-44-44-20-4-4404-22222-2-20002-2000000200-20022−22−222200−22−222−22−2000000000000000000000000000000
χ784-4-44-44-20-4-4404-22222-2-20002-2000000200-200−222222−22002−22−2−22−22000000000000000000000000000000
χ798-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000

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