Finite Group Databasebeta

← Group #10691237

Character table — Group #10691237

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121216161616161616161616242424242424242424244848
order1222222222366644446666661212121244448888121224242424242424244444441212121212121212224444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1
χ911111-1-1-11-1111111-1-111-1-1-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-11-1-1-111ii−i−i1-1ii−i−iii−i−i1-1
χ1011111-1-1-11-1111111-1-111-1-1-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i-1-1111-1-1-111ii−i−i-11−i−iii−i−iii-11
χ1111111-1-1-11-1111111-1-111-1-1-1-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii11-1-1-1111-1-1ii−i−i1-1ii−i−i−i−iii-11
χ1211111-1-1-11-1111111-1-111-1-1-1-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-1-111-1111-1-1ii−i−i-11−i−iiiii−i−i1-1
χ1311111-1-1-11-1111111-1-111-1-1-1-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i11-1-1-1111-1-1−i−iii1-1−i−iiiii−i−i-11
χ1411111-1-1-11-1111111-1-111-1-1-1-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-1-111-1111-1-1−i−iii-11ii−i−i−i−iii1-1
χ1511111-1-1-11-1111111-1-111-1-1-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-11-1-1-111−i−iii1-1−i−iii−i−iii1-1
χ1611111-1-1-11-1111111-1-111-1-1-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii-1-1111-1-1-111−i−iii-11ii−i−iii−i−i-11
χ1722222222222222-2-2-2-2222222-2-2-2-200000000-2-20000000022220000000000-2-20000000000
χ1822222222222222-2-2-2-2222222-2-2-2-200000000-2-200000000-2-2-2-20000000000220000000000
χ192222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1-1-1000000000000
χ202222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1111111110000-2-21111-1-1-1-1000000000000
χ212222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10000-2-211111111000000000000
χ222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000022-1-1-1-11111000000000000
χ2322222-2-2-22-22222-2-22222-2-2-2-2-2-22200000000-220000000022-2-20000000000-220000000000
χ2422222-2-2-22-22222-2-22222-2-2-2-2-2-22200000000-2200000000-2-22200000000002-20000000000
χ2522222-2-2-22-2-1-1-1-122-2-2-1-11111-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii00002-211-1-1−i−iii000000000000
χ2622222-2-2-22-2-1-1-1-122-2-2-1-11111-1-1112i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i0000-22-1-111−i−iii000000000000
χ2722222-2-2-22-2-1-1-1-122-2-2-1-11111-1-111−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii0000-22-1-111ii−i−i000000000000
χ2822222-2-2-22-2-1-1-1-122-2-2-1-11111-1-111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i00002-211-1-1ii−i−i000000000000
χ292222-222-2-2-222222-22-2-2-222-2-2222200000000-2-20000000000000000000000002i−2i2i−2i000000
χ302222-222-2-2-222222-22-2-2-222-2-2222200000000-2-2000000000000000000000000−2i2i−2i2i000000
χ312222-222-2-2-22222-22-22-2-222-2-2-2-2-2-22i−2i2i−2i0000220000000000000000002i−2i2i−2i000000000000
χ322222-222-2-2-22222-22-22-2-222-2-2-2-2-2-2−2i2i−2i2i000022000000000000000000−2i2i−2i2i000000000000
χ332222-222-2-2-2-1-1-1-1-22-2211-1-11111112i−2i2i−2i0000-1-133−3−333−3−3000000−i3i3−i3i3−ii−ii000000000000
χ342222-222-2-2-2-1-1-1-1-22-2211-1-11111112i−2i2i−2i0000-1-1−3−333−3−333000000i3−i3i3−i3−ii−ii000000000000
χ352222-222-2-2-2-1-1-1-1-22-2211-1-1111111−2i2i−2i2i0000-1-133−3−333−3−3000000i3−i3i3−i3i−ii−i000000000000
χ362222-222-2-2-2-1-1-1-1-22-2211-1-1111111−2i2i−2i2i0000-1-1−3−333−3−333000000−i3i3−i3i3i−ii−i000000000000
χ372222-2-2-22-2222222-2-22-2-2-2-22222-2-200000000-220000000000000000000000002-2-22000000
χ382222-2-2-22-2222222-2-22-2-2-2-22222-2-200000000-22000000000000000000000000-222-2000000
χ392222-2-2-22-222222-222-2-2-2-2-222-2-2222-2-2200002-20000000000000000002-2-22000000000000
χ402222-2-2-22-222222-222-2-2-2-2-222-2-222-222-200002-2000000000000000000-222-2000000000000
χ412222-2-2-22-22-1-1-1-1-222-21111-1-111-1-12-2-220000-11−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3-111-1000000000000
χ422222-2-2-22-22-1-1-1-1-222-21111-1-111-1-12-2-220000-11i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3-111-1000000000000
χ432222-2-2-22-22-1-1-1-1-222-21111-1-111-1-1-222-20000-11−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i31-1-11000000000000
χ442222-2-2-22-22-1-1-1-1-222-21111-1-111-1-1-222-20000-11i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i31-1-11000000000000
χ4522-2-2-22-222-222-2-200002-22-2-2200000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i00000000000000002−22−200
χ4622-2-2-22-222-222-2-200002-22-2-2200000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i0000000000000000−22−2200
χ4722-2-2-22-222-222-2-200002-22-2-2200000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i0000000000000000−22−2200
χ4822-2-2-22-222-222-2-200002-22-2-2200000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i00000000000000002−22−200
χ4922-2-2-2-22-22222-2-200002-2-222-2000000002−2−22002−22−2−22−222i−2i−2i2i0000000000000000i2−i2−i2i200
χ5022-2-2-2-22-22222-2-200002-2-222-2000000002−2−22002−22−2−22−22−2i2i2i−2i0000000000000000−i2i2i2−i200
χ5122-2-2-2-22-22222-2-200002-2-222-200000000−222−200−22−222−22−22i−2i−2i2i0000000000000000−i2i2i2−i200
χ5222-2-2-2-22-22222-2-200002-2-222-200000000−222−200−22−222−22−2−2i2i2i−2i0000000000000000i2−i2−i2i200
χ534444444444-2-2-2-2-4-4-4-4-2-2-2-2-2-2222200000000220000000000000000000000000000000000
χ5444444-4-4-44-4-2-2-2-2-4-444-2-2222222-2-2000000002-20000000000000000000000000000000000
χ554444-444-4-4-4-2-2-2-24-44-422-2-222-2-2-2-200000000220000000000000000000000000000000000
χ564444-4-4-44-44-2-2-2-24-4-442222-2-2-2-222000000002-20000000000000000000000000000000000
χ5744-4-444-4-4-4444-4-40000-444-44-4000000000000000000000000000000000000000000000000
χ5844-4-444-4-4-44-2-22200002-2-22-2200000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ5944-4-444-4-4-44-2-22200002-2-22-2200000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ6044-4-44-444-4-444-4-40000-44-44-44000000000000000000000000000000000000000000000000
χ6144-4-44-444-4-4-2-22200002-22-22-2000000000000006−6−66−666−600000000000000000000000000
χ6244-4-44-444-4-4-2-22200002-22-22-200000000000000−666−66−6−6600000000000000000000000000
χ6344-4-4-44-444-4-2-2220000-22-222-200000000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ6444-4-4-44-444-4-2-2220000-22-222-2000000002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ6544-4-4-4-44-444-2-2220000-222-2-220000000022−22−222200−22−222−22−200000000000000000000000000
χ6644-4-4-4-44-444-2-2220000-222-2-2200000000−222222−22002−22−2−22−2200000000000000000000000000
χ678-88-80000008-8-880000000000000000000000000000000000000000000000000000000000
χ688-88-8000000-444-40000000000−4i34i30000000000000000000000000000000000000000000000
χ698-88-8000000-444-400000000004i3−4i30000000000000000000000000000000000000000000000
χ708-8-880000008-88-80000000000000000000000000000000000000000000000000000000000
χ718-8-88000000-44-4400000000000043−4300000000000000000000000000000000000000000000
χ728-8-88000000-44-44000000000000−434300000000000000000000000000000000000000000000

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