Finite Group Databasebeta

← Group #10711557

Character table — Group #10711557

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order122222344446668888668812121212161616161616161624242424444488882424484848484848484844881616161616161616448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-11-111-11111111-1-1-1-11-11-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101111-1-11-111-11111111-1-1-1-11-11-11111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111111-1-11-111-11111111-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121111-1-11-111-11111111-1-1-1-11-11-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131111-1-11-111-11111111-1-1-1-11-11-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141111-1-11-111-11111111-1-1-1-11-11-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151111-1-11-111-11111111-1-1-1-11-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161111-1-11-111-11111111-1-1-1-11-11-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ1722222222222222-2-2-2-222-2-2222200000000-2-2-2-22222-2-2-2-2-2-20000000022-2-2000000000000000000000000
χ1822222222222222-2-2-2-222-2-2222200000000-2-2-2-2-2-2-2-22222-2-200000000-2-222000000000000000000000000
χ192222222-2-2-2-222200002200-2-2-2-2−i2−i2i2i2−i2−i2i2i2000022-2-2000000−i2−i2i2i2−i2−i2i2i22-200−i2−i2i2i2−i2−i2i2i20000000000000000
χ202222222-2-2-2-222200002200-2-2-2-2−i2−i2i2i2−i2−i2i2i20000-2-222000000−i2−i2i2i2−i2−i2i2i2-2200i2i2−i2−i2i2i2−i2−i20000000000000000
χ212222222-2-2-2-222200002200-2-2-2-2i2i2−i2−i2i2i2−i2−i2000022-2-2000000i2i2−i2−i2i2i2−i2−i22-200i2i2−i2−i2i2i2−i2−i20000000000000000
χ222222222-2-2-2-222200002200-2-2-2-2i2i2−i2−i2i2i2−i2−i20000-2-222000000i2i2−i2−i2i2i2−i2−i2-2200−i2−i2i2i2−i2−i2i2i20000000000000000
χ23222222-12222-1-1-12222-1-122-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ24222222-12222-1-1-12222-1-122-1-1-1-122222222-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ25222222-12222-1-1-12222-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ26222222-12222-1-1-12222-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ272222-2-222-2-222220000-2-200-22-22−i2−i2i2i2i2i2−i2−i2000022-2-2000000−i2−i2i2i2i2i2−i2−i2-2200−i2−i2i2i2i2i2−i2−i20000000000000000
χ282222-2-222-2-222220000-2-200-22-22−i2−i2i2i2i2i2−i2−i20000-2-222000000−i2−i2i2i2i2i2−i2−i22-200i2i2−i2−i2−i2−i2i2i20000000000000000
χ292222-2-222-2-222220000-2-200-22-22i2i2−i2−i2−i2−i2i2i2000022-2-2000000i2i2−i2−i2−i2−i2i2i2-2200i2i2−i2−i2−i2−i2i2i20000000000000000
χ302222-2-222-2-222220000-2-200-22-22i2i2−i2−i2−i2−i2i2i20000-2-222000000i2i2−i2−i2−i2−i2i2i22-200−i2−i2i2i2i2i2−i2−i20000000000000000
χ312222-2-22-222-2222-2-2-2-2-2-2222-22-200000000-2-2-2-22222-2-2-2-22200000000-2-222000000000000000000000000
χ322222-2-22-222-2222-2-2-2-2-2-2222-22-200000000-2-2-2-2-2-2-2-22222220000000022-2-2000000000000000000000000
χ332222-2-2-1-222-2-1-1-1222211-2-2-11-112222-2-2-2-2-1-1-1-10000000011-1-1-1-111110000000000002i−2i2i−2i−i−iii−i−iii0000
χ342222-2-2-1-222-2-1-1-1222211-2-2-11-112222-2-2-2-2-1-1-1-10000000011-1-1-1-11111000000000000−2i2i−2i2iii−i−iii−i−i0000
χ352222-2-2-1-222-2-1-1-1222211-2-2-11-11-2-2-2-22222-1-1-1-100000000111111-1-1-1-10000000000002i−2i−2i2i−i−iiiii−i−i0000
χ362222-2-2-1-222-2-1-1-1222211-2-2-11-11-2-2-2-22222-1-1-1-100000000111111-1-1-1-1000000000000−2i2i2i−2iii−i−i−i−iii0000
χ3722-2-22-222-22-2-2-2200002-20022-2-22−22−22−22−20000000022-2-2002−22−22−22−2002-22−22−22−22−20000000000000000
χ3822-2-22-222-22-2-2-2200002-20022-2-22−22−22−22−200000000-2-222002−22−22−22−200-22−22−22−22−220000000000000000
χ3922-2-22-222-22-2-2-2200002-20022-2-2−22−22−22−220000000022-2-200−22−22−22−22002-2−22−22−22−220000000000000000
χ4022-2-22-222-22-2-2-2200002-20022-2-2−22−22−22−2200000000-2-22200−22−22−22−2200-222−22−22−22−20000000000000000
χ4122-2-22-22-22-22-2-2222-2-22-22-2-2-22200000000-2-222000000002-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ4222-2-22-22-22-22-2-2222-2-22-22-2-2-22200000000-2-222000000002-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4322-2-22-22-22-22-2-22-2-2222-2-22-2-2222i−2i−2i2i2i−2i−2i2i22-2-200000000-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ4422-2-22-22-22-22-2-22-2-2222-2-22-2-222−2i2i2i−2i−2i2i2i−2i22-2-200000000-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ4522-2-22-2-1-22-2211-1-2-222-11-2211-1-12i−2i−2i2i2i−2i−2i2i-1-111000000001-1−iii−i−iii−i00000000000000003−33−3−i3i3−i3i30000
χ4622-2-22-2-1-22-2211-1-2-222-11-2211-1-12i−2i−2i2i2i−2i−2i2i-1-111000000001-1−iii−i−iii−i0000000000000000−33−33i3−i3i3−i30000
χ4722-2-22-2-1-22-2211-1-2-222-11-2211-1-1−2i2i2i−2i−2i2i2i−2i-1-111000000001-1i−i−iii−i−ii00000000000000003−33−3i3−i3i3−i30000
χ4822-2-22-2-1-22-2211-1-2-222-11-2211-1-1−2i2i2i−2i−2i2i2i−2i-1-111000000001-1i−i−iii−i−ii0000000000000000−33−33−i3i3−i3i30000
χ4922-2-2-22222-2-2-2-2222-2-2-22-22-222-200000000-2-22200000000-220000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5022-2-2-22222-2-2-2-2222-2-2-22-22-222-200000000-2-22200000000-22000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ5122-2-2-22222-2-2-2-22-2-222-222-2-222-22i−2i−2i2i−2i2i2i−2i22-2-2000000002-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ5222-2-2-22222-2-2-2-22-2-222-222-2-222-2−2i2i2i−2i2i−2i−2i2i22-2-2000000002-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ5322-2-2-222-2-222-2-220000-22002-2-222−22−2−22−220000000022-2-2002−22−2−22−2200-222−22−2−22−220000000000000000
χ5422-2-2-222-2-222-2-220000-22002-2-222−22−2−22−2200000000-2-222002−22−2−22−22002-2−22−222−22−20000000000000000
χ5522-2-2-222-2-222-2-220000-22002-2-22−22−222−22−20000000022-2-200−22−222−22−200-22−22−222−22−20000000000000000
χ5622-2-2-222-2-222-2-220000-22002-2-22−22−222−22−200000000-2-22200−22−222−22−2002-22−22−2−22−220000000000000000
χ5722-2-2-22-122-2-211-1-2-2221-12-21-1-112i−2i−2i2i−2i2i2i−2i-1-11100000000-11−iii−ii−i−ii0000000000000000−i3i3i3−i3−333−30000
χ5822-2-2-22-122-2-211-1-2-2221-12-21-1-112i−2i−2i2i−2i2i2i−2i-1-11100000000-11−iii−ii−i−ii0000000000000000i3−i3−i3i33−3−330000
χ5922-2-2-22-122-2-211-1-2-2221-12-21-1-11−2i2i2i−2i2i−2i−2i2i-1-11100000000-11i−i−ii−iii−i0000000000000000−i3i3i3−i33−3−330000
χ6022-2-2-22-122-2-211-1-2-2221-12-21-1-11−2i2i2i−2i2i−2i−2i2i-1-11100000000-11i−i−ii−iii−i0000000000000000i3−i3−i3i3−333−30000
χ61444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-20000000022220000000022000000000000000000000000000000000000
χ62444444-2-4-4-4-4-2-2-20000-2-2002222−2i2−2i22i22i2−2i2−2i22i22i200000000000000i2i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ63444444-2-4-4-4-4-2-2-20000-2-20022222i22i2−2i2−2i22i22i2−2i2−2i200000000000000−i2−i2i2i2−i2−i2i2i20000000000000000000000000000
χ644444-4-4-24-4-44-2-2-2000022002-22-2−2i2−2i22i22i22i22i2−2i2−2i200000000000000i2i2−i2−i2−i2−i2i2i20000000000000000000000000000
χ654444-4-4-24-4-44-2-2-2000022002-22-22i22i2−2i2−2i2−2i2−2i22i22i200000000000000−i2−i2i2i2i2i2−i2−i20000000000000000000000000000
χ664444-4-4-2-444-4-2-2-2-4-4-4-42244-22-2200000000222200000000-2-2000000000000000000000000000000000000
χ6744-4-44-4-24-44-422-20000-2200-2-22222−2222−2222−2222−2200000000000000−22−22−22−220000000000000000000000000000
χ6844-4-44-4-24-44-422-20000-2200-2-222−2222−2222−2222−2222000000000000002−22−22−22−20000000000000000000000000000
χ6944-4-44-4-2-44-4422-244-4-4-224-422-2-20000000022-2-200000000-22000000000000000000000000000000000000
χ7044-4-4-44-244-4-422-244-4-42-2-442-2-220000000022-2-2000000002-2000000000000000000000000000000000000
χ7144-4-4-44-2-4-44422-200002-200-222-222−2222−22−2222−222200000000000000−22−222−22−20000000000000000000000000000
χ7244-4-4-44-2-4-44422-200002-200-222-2−2222−222222−2222−22000000000000002−22−2−22−220000000000000000000000000000
χ734-44-400400004-4-4−2i22i2−2i22i20000000000000000−2i22i2−2i22i2004-4−2i22i2−2i22i200000000000000000000000000000000000000
χ744-44-400400004-4-4−2i22i2−2i22i20000000000000000−2i22i2−2i22i200-442i2−2i22i2−2i200000000000000000000000000000000000000
χ754-44-400400004-4-42i2−2i22i2−2i200000000000000002i2−2i22i2−2i2004-42i2−2i22i2−2i200000000000000000000000000000000000000
χ764-44-400400004-4-42i2−2i22i2−2i200000000000000002i2−2i22i2−2i200-44−2i22i2−2i22i200000000000000000000000000000000000000
χ774-4-440040000-44-4−2i22i22i2−2i200000000000000002i2−2i2−2i22i24-400−2i22i22i2−2i200000000000000000000000000000000000000
χ784-4-440040000-44-4−2i22i22i2−2i200000000000000002i2−2i2−2i22i2-44002i2−2i2−2i22i200000000000000000000000000000000000000
χ794-4-440040000-44-42i2−2i2−2i22i20000000000000000−2i22i22i2−2i24-4002i2−2i2−2i22i200000000000000000000000000000000000000
χ804-4-440040000-44-42i2−2i2−2i22i20000000000000000−2i22i22i2−2i2-4400−2i22i22i2−2i200000000000000000000000000000000000000
χ818-88-800-40000-444−4i24i2−4i24i200000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ828-88-800-40000-4444i2−4i24i2−4i20000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ838-8-8800-400004-44−4i24i24i2−4i20000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ848-8-8800-400004-444i2−4i2−4i24i200000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000000000

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