Finite Group Databasebeta

← Group #10692945

Character table — Group #10692945

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order1222222222344666444666666888888881212121212122424242424242424224444448888888844441212121212121212444444
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
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ911111-1-11-1-11-1-111111-11-1-1-11-1iiii−i−i−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1i−i
χ1011111-1-11-1-11-1-111111-11-1-1-11-1iiii−i−i−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii-1-111−i−iii-1-111−ii
χ1111111-1-11-1-11-1-111111-11-1-1-11-1iiii−i−i−i−i11-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−i11-1-1ii−i−i-1-111−ii
χ1211111-1-11-1-11-1-111111-11-1-1-11-1iiii−i−i−i−i11-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii-1-111−i−iii11-1-1i−i
χ1311111-1-11-1-11-1-111111-11-1-1-11-1−i−i−i−iiiii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1−ii
χ1411111-1-11-1-11-1-111111-11-1-1-11-1−i−i−i−iiiii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11i−i-1-111ii−i−i-1-111i−i
χ1511111-1-11-1-11-1-111111-11-1-1-11-1−i−i−i−iiiii11-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1−ii11-1-1−i−iii-1-111i−i
χ1611111-1-11-1-11-1-111111-11-1-1-11-1−i−i−i−iiiii11-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-11i−i-1-111ii−i−i11-1-1−ii
χ1722222222222-2-2222-2-2-222222200000000-2-2-2-2-2-20000000022-2-222-2-200000000000000000000000000
χ1822222222222-2-2222-2-2-222222200000000-2-2-2-2-2-200000000-2-222-2-22200000000000000000000000000
χ192222222222-122-1-1-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ202222222222-122-1-1-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ212222222222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ222222222222-122-1-1-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ2322222-2-22-2-2222222-2-222-2-2-22-200000000-2-222-220000000022-2-2-2-22200000000000000000000000000
χ2422222-2-22-2-2222222-2-222-2-2-22-200000000-2-222-2200000000-2-22222-2-200000000000000000000000000
χ2522222-2-22-2-2-1-2-2-1-1-122-2-1111-112i2i2i2i−2i−2i−2i−2i-1-111-11−i−i−i−iiiii00000000000000002-22i−2i-1-111−i−iii000000
χ2622222-2-22-2-2-1-2-2-1-1-122-2-1111-112i2i2i2i−2i−2i−2i−2i-1-111-11−i−i−i−iiiii0000000000000000-22−2i2i11-1-1ii−i−i000000
χ2722222-2-22-2-2-1-2-2-1-1-122-2-1111-11−2i−2i−2i−2i2i2i2i2i-1-111-11iiii−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i000000
χ2822222-2-22-2-2-1-2-2-1-1-122-2-1111-11−2i−2i−2i−2i2i2i2i2i-1-111-11iiii−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii000000
χ292222-22-2-22-22222222-2-2-22-2-2-2200000000-2-2222-2000000000000000022-2-222-2-2000000000000000000
χ302222-22-2-22-22222222-2-2-22-2-2-2200000000-2-2222-20000000000000000-2-222-2-222000000000000000000
χ312222-22-2-22-22-2-2222-222-22-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ322222-22-2-22-22-2-2222-222-22-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000
χ332222-22-2-22-2-1-2-2-1-1-1-2221-1111-12i2i−2i−2i2i2i−2i−2i-1-1111-1−i−iii−i−iii000000000000000000003−33−3−i3i3−i3i3000000
χ342222-22-2-22-2-1-2-2-1-1-1-2221-1111-12i2i−2i−2i2i2i−2i−2i-1-1111-1−i−iii−i−iii00000000000000000000−33−33i3−i3i3−i3000000
χ352222-22-2-22-2-1-2-2-1-1-1-2221-1111-1−2i−2i2i2i−2i−2i2i2i-1-1111-1ii−i−iii−i−i000000000000000000003−33−3i3−i3i3−i3000000
χ362222-22-2-22-2-1-2-2-1-1-1-2221-1111-1−2i−2i2i2i−2i−2i2i2i-1-1111-1ii−i−iii−i−i00000000000000000000−33−33−i3i3−i3i3000000
χ372222-2-22-2-22222222-22-2-2-222-2-222-2-2-2-2222222-2-222-2-2-2-2220000000000000000000000000000000000
χ382222-2-22-2-22222222-22-2-2-222-2-2-2-22222-2-22222-2-2-2-22222-2-20000000000000000000000000000000000
χ392222-2-22-2-222-2-22222-22-2-222-2-200000000-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ402222-2-22-2-222-2-22222-22-2-222-2-200000000-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ412222-2-22-2-22-122-1-1-1-22-211-1-11122-2-2-2-222-1-1-1-111-1-11111-1-1000000000000000000003−3−33−333−3000000
χ422222-2-22-2-22-122-1-1-1-22-211-1-11122-2-2-2-222-1-1-1-111-1-11111-1-100000000000000000000−333−33−3−33000000
χ432222-2-22-2-22-122-1-1-1-22-211-1-111-2-22222-2-2-1-1-1-11111-1-1-1-111000000000000000000003−3−333−3−33000000
χ442222-2-22-2-22-122-1-1-1-22-211-1-111-2-22222-2-2-1-1-1-11111-1-1-1-11100000000000000000000−333−3−333−3000000
χ4522-2-2222-2-2-22002-2-2000222-2-2-22−22−22−22−20000002−22−22−22−22-2002-2002−22−22−22−2000000000000000000
χ4622-2-2222-2-2-22002-2-2000222-2-2-22−22−22−22−20000002−22−22−22−2-2200-2200−22−22−22−22000000000000000000
χ4722-2-2222-2-2-22002-2-2000222-2-2-2−22−22−22−22000000−22−22−22−222-2002-200−22−22−22−22000000000000000000
χ4822-2-2222-2-2-22002-2-2000222-2-2-2−22−22−22−22000000−22−22−22−22-2200-22002−22−22−22−2000000000000000000
χ4922-2-22-2-2-2222002-2-20002-2-22-22−i2i2−i2i2i2−i2i2−i2000000−i2i2−i2i2i2−i2i2−i22-200-2200−i2i2−i2i2i2−i2i2−i2000000000000000000
χ5022-2-22-2-2-2222002-2-20002-2-22-22−i2i2−i2i2i2−i2i2−i2000000−i2i2−i2i2i2−i2i2−i2-22002-200i2−i2i2−i2−i2i2−i2i2000000000000000000
χ5122-2-22-2-2-2222002-2-20002-2-22-22i2−i2i2−i2−i2i2−i2i2000000i2−i2i2−i2−i2i2−i2i22-200-2200i2−i2i2−i2−i2i2−i2i2000000000000000000
χ5222-2-22-2-2-2222002-2-20002-2-22-22i2−i2i2−i2−i2i2−i2i2000000i2−i2i2−i2−i2i2−i2i2-22002-200−i2i2−i2i2i2−i2i2−i2000000000000000000
χ5322-2-2-22-22-222002-2-2000-22-222-2−i2i2i2−i2−i2i2i2−i2000000−i2i2i2−i2−i2i2i2−i2002i−2i002i−2i2−2−222−2−22000000000000000000
χ5422-2-2-22-22-222002-2-2000-22-222-2−i2i2i2−i2−i2i2i2−i2000000−i2i2i2−i2−i2i2i2−i200−2i2i00−2i2i−222−2−222−2000000000000000000
χ5522-2-2-22-22-222002-2-2000-22-222-2i2−i2−i2i2i2−i2−i2i2000000i2−i2−i2i2i2−i2−i2i2002i−2i002i−2i−222−2−222−2000000000000000000
χ5622-2-2-22-22-222002-2-2000-22-222-2i2−i2−i2i2i2−i2−i2i2000000i2−i2−i2i2i2−i2−i2i200−2i2i00−2i2i2−2−222−2−22000000000000000000
χ5722-2-2-2-2222-22002-2-2000-2-22-2222−2−22−222−20000002−2−22−222−2002i−2i00−2i2ii2−i2−i2i2−i2i2i2−i2000000000000000000
χ5822-2-2-2-2222-22002-2-2000-2-22-2222−2−22−222−20000002−2−22−222−200−2i2i002i−2i−i2i2i2−i2i2−i2−i2i2000000000000000000
χ5922-2-2-2-2222-22002-2-2000-2-22-222−222−22−2−22000000−222−22−2−22002i−2i00−2i2i−i2i2i2−i2i2−i2−i2i2000000000000000000
χ6022-2-2-2-2222-22002-2-2000-2-22-222−222−22−2−22000000−222−22−2−2200−2i2i002i−2ii2−i2−i2i2−i2i2i2−i2000000000000000000
χ614444444444-2-4-4-2-2-2-4-4-4-2-2-2-2-2-200000000222222000000000000000000000000000000000000000000
χ6244444-4-44-4-4-244-2-2-2-4-44-2222-220000000022-2-22-2000000000000000000000000000000000000000000
χ634444-44-4-44-4-244-2-2-24-4-42-2222-20000000022-2-2-22000000000000000000000000000000000000000000
χ644444-4-44-4-44-2-4-4-2-2-24-4422-2-222000000002222-2-2000000000000000000000000000000000000000000
χ6544-4-4444-4-4-4-200-222000-2-2-222222−2222−2222−2222−22000000−22−22−22−220000000000000000000000000000000000
χ6644-4-4444-4-4-4-200-222000-2-2-2222−2222−2222−2222−22220000002−22−22−22−20000000000000000000000000000000000
χ6744-4-44-4-4-444-200-222000-222-22-2−2i22i2−2i22i22i2−2i22i2−2i2000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000000000
χ6844-4-44-4-4-444-200-222000-222-22-22i2−2i22i2−2i2−2i22i2−2i22i2000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000000000
χ6944-4-4-44-44-44-200-2220002-22-2-22−2i22i22i2−2i2−2i22i22i2−2i2000000i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ7044-4-4-44-44-44-200-2220002-22-2-222i2−2i2−2i22i22i2−2i2−2i22i2000000−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ7144-4-4-4-4444-4-200-22200022-22-2-222−22−2222−222222−22000000−222−22−2−220000000000000000000000000000000000
χ7244-4-4-4-4444-4-200-22200022-22-2-2−222222−2222−22−22220000002−2−22−222−20000000000000000000000000000000000
χ734-4-4400000044-4-4-4400000000000000000004-4000000000000000000000000000000000000002-22-200
χ744-4-4400000044-4-4-4400000000000000000004-400000000000000000000000000000000000000-22-2200
χ754-4-440000004-44-4-440000000000000000000-44000000000000000000000000000000000000002-2-2200
χ764-4-440000004-44-4-440000000000000000000-4400000000000000000000000000000000000000-222-200
χ778-88-8000000800-88-800000000000000000000000000000000000000000000000000000000000000000
χ788-88-8000000-4004-440000000000000000043−430000000000000000000000000000000000000000000000
χ798-88-8000000-4004-4400000000000000000−43430000000000000000000000000000000000000000000000
χ808-8-88000000-48-844-40000000000000000000-4400000000000000000000000000000000000000000000
χ818-8-88000000-4-8844-400000000000000000004-400000000000000000000000000000000000000000000

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