Finite Group Databasebeta

← Group #10692025

Character table — Group #10692025

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order12222234444446664446688888888121212121212121212122424242424242424224444448888888888882424242424242424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ91111-1-111-11-1-1-111111-1-1-1iiii−i−i−i−i111-1-11-1-11-1iiii−i−i−i−i11-1-1-1-111ii−i−iii−i−ii−i1-1ii−i−i11-1-1ii−i−i1-1
χ101111-1-111-11-1-1-111111-1-1-1iiii−i−i−i−i111-1-11-1-11-1iiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i−ii-11−i−iii-1-111−i−iii-11
χ111111-1-111-11-1-1-111111-1-1-1iiii−i−i−i−i111-1-11-1-11-1iiii−i−i−i−i-1-11111-1-1−i−iii−i−iiii−i1-1ii−i−i11-1-1−i−iii-11
χ121111-1-111-11-1-1-111111-1-1-1iiii−i−i−i−i111-1-11-1-11-1iiii−i−i−i−i-1-11111-1-1−i−iii−i−iii−ii-11−i−iii-1-111ii−i−i1-1
χ131111-1-111-11-1-1-111111-1-1-1−i−i−i−iiiii111-1-11-1-11-1−i−i−i−iiiii11-1-1-1-111−i−iii−i−iiii−i-11ii−i−i-1-111ii−i−i-11
χ141111-1-111-11-1-1-111111-1-1-1−i−i−i−iiiii111-1-11-1-11-1−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii−ii1-1−i−iii11-1-1−i−iii1-1
χ151111-1-111-11-1-1-111111-1-1-1−i−i−i−iiiii111-1-11-1-11-1−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−ii−i-11ii−i−i-1-111−i−iii1-1
χ161111-1-111-11-1-1-111111-1-1-1−i−i−i−iiiii111-1-11-1-11-1−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i−ii1-1−i−iii11-1-1ii−i−i-11
χ1722222222222-2-2222-2-2-222000000002-2-22-222-2-2-2000000002222-2-2-2-200000000000000000000000000
χ1822222222222-2-2222-2-2-222000000002-2-22-222-2-2-200000000-2-2-2-2222200000000000000000000000000
χ192222222-2-2-2-2222222-2-22222-2-222-2-2-222-22-2-22-2-222-2-222-2-20000000000000000000000000000000000
χ202222222-2-2-2-2222222-2-222-2-222-2-222-222-22-2-22-2-2-2-222-2-2220000000000000000000000000000000000
χ212222222-2-2-2-2-2-2222-2222200000000-2-2-2-2-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ222222222-2-2-2-2-2-2222-2222200000000-2-2-2-2-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ23222222-1222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ24222222-1222222-1-1-1222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ25222222-1222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ26222222-1222222-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ27222222-1-2-2-2-222-1-1-12-2-2-1-122-2-222-2-21-1-11-111-111-1-111-1-111000000000000000000003−33−33−33−3000000
χ28222222-1-2-2-2-222-1-1-12-2-2-1-122-2-222-2-21-1-11-111-111-1-111-1-11100000000000000000000−33−33−33−33000000
χ29222222-1-2-2-2-222-1-1-12-2-2-1-1-2-222-2-2221-1-11-111-11111-1-111-1-1000000000000000000003−33−3−33−33000000
χ30222222-1-2-2-2-222-1-1-12-2-2-1-1-2-222-2-2221-1-11-111-11111-1-111-1-100000000000000000000−33−333−33−3000000
χ312222-2-222-22-222222-2-22-2-2000000002-2-2-222-22-220000000022-2-222-2-200000000000000000000000000
χ322222-2-222-22-222222-2-22-2-2000000002-2-2-222-22-2200000000-2-222-2-22200000000000000000000000000
χ332222-2-22-22-2222222-22-2-2-200000000-2-2-222-2222-200000000000000002222-2-2-2-2000000000000000000
χ342222-2-22-22-2222222-22-2-2-200000000-2-2-222-2222-20000000000000000-2-2-2-22222000000000000000000
χ352222-2-22-22-22-2-22222-22-2-22i2i−2i−2i−2i−2i2i2i-2222-2-22-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ362222-2-22-22-22-2-22222-22-2-2−2i−2i2i2i2i2i−2i−2i-2222-2-22-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ372222-2-2-12-22-2-2-2-1-1-122-2112i2i2i2i−2i−2i−2i−2i-1-1-111-111-11−i−i−i−iiiii00000000000000002i−2i2-2−i−iii-1-111000000
χ382222-2-2-12-22-2-2-2-1-1-122-2112i2i2i2i−2i−2i−2i−2i-1-1-111-111-11−i−i−i−iiiii0000000000000000−2i2i-22ii−i−i11-1-1000000
χ392222-2-2-12-22-2-2-2-1-1-122-211−2i−2i−2i−2i2i2i2i2i-1-1-111-111-11iiii−i−i−i−i00000000000000002i−2i-22−i−iii11-1-1000000
χ402222-2-2-12-22-2-2-2-1-1-122-211−2i−2i−2i−2i2i2i2i2i-1-1-111-111-11iiii−i−i−i−i0000000000000000−2i2i2-2ii−i−i-1-111000000
χ412222-2-2-1-22-22-2-2-1-1-12-22112i2i−2i−2i−2i−2i2i2i1-1-1-111-111-1−i−iiiii−i−i00000000000000000000−i3i3i3−i3−333−3000000
χ422222-2-2-1-22-22-2-2-1-1-12-22112i2i−2i−2i−2i−2i2i2i1-1-1-111-111-1−i−iiiii−i−i00000000000000000000i3−i3−i3i33−3−33000000
χ432222-2-2-1-22-22-2-2-1-1-12-2211−2i−2i2i2i2i2i−2i−2i1-1-1-111-111-1ii−i−i−i−iii00000000000000000000−i3i3i3−i33−3−33000000
χ442222-2-2-1-22-22-2-2-1-1-12-2211−2i−2i2i2i2i2i−2i−2i1-1-1-111-111-1ii−i−i−i−iii00000000000000000000i3−i3−i3i3−333−3000000
χ4522-2-22-2222-2-2002-2-20002-22−22−22−22−220020-2-20002−22−22−22−22-22-200002−22−22−22−2000000000000000000
χ4622-2-22-2222-2-2002-2-20002-22−22−22−22−220020-2-20002−22−22−22−2-22-220000−22−22−22−22000000000000000000
χ4722-2-22-2222-2-2002-2-20002-2−22−22−22−2220020-2-2000−22−22−22−222-22-20000−22−22−22−22000000000000000000
χ4822-2-22-2222-2-2002-2-20002-2−22−22−22−2220020-2-2000−22−22−22−22-22-2200002−22−22−22−2000000000000000000
χ4922-2-22-22-2-222002-2-20002-22−2−222−2−22-200-20220002−2−222−2−2200002i−2i2i−2i−i2i2i2−i2i2−i2−i2i2000000000000000000
χ5022-2-22-22-2-222002-2-20002-22−2−222−2−22-200-20220002−2−222−2−220000−2i2i−2i2ii2−i2−i2i2−i2i2i2−i2000000000000000000
χ5122-2-22-22-2-222002-2-20002-2−222−2−222−2-200-2022000−222−2−222−200002i−2i2i−2ii2−i2−i2i2−i2i2i2−i2000000000000000000
χ5222-2-22-22-2-222002-2-20002-2−222−2−222−2-200-2022000−222−2−222−20000−2i2i−2i2i−i2i2i2−i2i2−i2−i2i2000000000000000000
χ5322-2-2-2222-2-22002-2-2000-22−i2i2−i2i2i2−i2i2−i2200-20-22000−i2i2−i2i2i2−i2i2−i22-2-220000−i2i2i2−i2−i2i2i2−i2000000000000000000
χ5422-2-2-2222-2-22002-2-2000-22−i2i2−i2i2i2−i2i2−i2200-20-22000−i2i2−i2i2i2−i2i2−i2-222-20000i2−i2−i2i2i2−i2−i2i2000000000000000000
χ5522-2-2-2222-2-22002-2-2000-22i2−i2i2−i2−i2i2−i2i2200-20-22000i2−i2i2−i2−i2i2−i2i22-2-220000i2−i2−i2i2i2−i2−i2i2000000000000000000
χ5622-2-2-2222-2-22002-2-2000-22i2−i2i2−i2−i2i2−i2i2200-20-22000i2−i2i2−i2−i2i2−i2i2-222-20000−i2i2i2−i2−i2i2i2−i2000000000000000000
χ5722-2-2-222-222-2002-2-2000-22−i2i2i2−i2i2−i2−i2i2-200202-2000−i2i2i2−i2i2−i2−i2i200002i−2i−2i2i2−22−2−22−22000000000000000000
χ5822-2-2-222-222-2002-2-2000-22−i2i2i2−i2i2−i2−i2i2-200202-2000−i2i2i2−i2i2−i2−i2i20000−2i2i2i−2i−22−222−22−2000000000000000000
χ5922-2-2-222-222-2002-2-2000-22i2−i2−i2i2−i2i2i2−i2-200202-2000i2−i2−i2i2−i2i2i2−i200002i−2i−2i2i−22−222−22−2000000000000000000
χ6022-2-2-222-222-2002-2-2000-22i2−i2−i2i2−i2i2i2−i2-200202-2000i2−i2−i2i2−i2i2i2−i20000−2i2i2i−2i2−22−2−22−22000000000000000000
χ61444444-24444-4-4-2-2-2-4-4-4-2-200000000-222-22-2-2222000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2-444-2-20000000022222222-2-2000000000000000000000000000000000000000000
χ634444-4-4-24-44-444-2-2-2-4-442200000000-2222-2-22-22-2000000000000000000000000000000000000000000
χ644444-4-4-2-44-4444-2-2-2-44-42200000000222-2-22-2-2-22000000000000000000000000000000000000000000
χ6544-4-44-4-244-4-400-222000-2222−2222−2222−2222−22-200-2022000−22−22−22−220000000000000000000000000000000000
χ6644-4-44-4-244-4-400-222000-22−2222−2222−2222−2222-200-20220002−22−22−22−20000000000000000000000000000000000
χ6744-4-44-4-2-4-44400-222000-2222−22−222222−22−222220020-2-2000−222−2−222−20000000000000000000000000000000000
χ6844-4-44-4-2-4-44400-222000-22−222222−22−222222−2220020-2-20002−2−222−2−220000000000000000000000000000000000
χ6944-4-4-44-24-4-4400-2220002-2−2i22i2−2i22i22i2−2i22i2−2i2-200202-2000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000000000
χ7044-4-4-44-24-4-4400-2220002-22i2−2i22i2−2i2−2i22i2−2i22i2-200202-2000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000000000
χ7144-4-4-44-2-444-400-2220002-2−2i22i22i2−2i22i2−2i2−2i22i2200-20-22000i2−i2−i2i2−i2i2i2−i20000000000000000000000000000000000
χ7244-4-4-44-2-444-400-2220002-22i2−2i2−2i22i2−2i22i22i2−2i2200-20-22000−i2i2i2−i2i2−i2−i2i20000000000000000000000000000000000
χ734-44-400400004-4-44-400000000000000000400-4000000000000000000000000000000000000002-22-200
χ744-44-400400004-4-44-400000000000000000400-400000000000000000000000000000000000000-22-2200
χ754-44-40040000-44-44-400000000000000000-4004000000000000000000000000000000000000002i−2i−2i2i00
χ764-44-40040000-44-44-400000000000000000-400400000000000000000000000000000000000000−2i2i2i−2i00
χ778-88-800-400008-84-4400000000000000000-400400000000000000000000000000000000000000000000
χ788-88-800-40000-884-4400000000000000000400-400000000000000000000000000000000000000000000
χ798-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-400000044-40000000000000043−430000000000000000000000000000000000000000000000000
χ818-8-8800-400000044-400000000000000−43430000000000000000000000000000000000000000000000000

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