Finite Group Databasebeta

← Group #10692947

Character table — Group #10692947

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222222234466666662244444444466661212121244446612121212121212121212121212121212888888888888888844121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1111-1-1111111111111-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1111-1-1111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911111-1-11-1-11-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1i−ii−i
χ1011111-1-11-1-11-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−ii−ii
χ1111111-1-11-1-11-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-1-111−ii−ii
χ1211111-1-11-1-11-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-1-111i−ii−i
χ1311111-1-11-1-11-1-11111111-1-1-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111i−i−ii
χ1411111-1-11-1-11-1-11111111-1-1-1-11111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−iii−i
χ1511111-1-11-1-11-1-11111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1−iii−i
χ1611111-1-11-1-11-1-11111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1i−i−ii
χ1722222222222-2-2222222222-2-222-2-2-2-2-22222-2-2-2-2000022-2-222-2-2-2-20000000000000000000000000000000000
χ1822222222222-2-22222222-2-222-2-2-2-2-2222222-2-2-2-20000-2-222-2-2-2-2220000000000000000000000000000000000
χ192222222222-122-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ202222222222-122-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ212222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2222-2-2-1-1-1-1-1-1-1-12222111111-1-111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ222222222222-122-1-1-1-1-1-1-1-2-2-2-2-2-2222-2-2-1-1-1-1-1-1-1-1-2-2-2-2111111-1-11111111111000000000000000022-1-1-1-10000
χ232222222222-1-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-2-1-1-1-111110000-1-111-1-11111−i3−i3i3i3−i3−i3i3i3000000000000000000−i3i3−i3i30000
χ242222222222-1-2-2-1-1-1-1-1-1-122-2-222-2-2-2-2-2-1-1-1-111110000-1-111-1-11111i3i3−i3−i3i3i3−i3−i3000000000000000000i3−i3i3−i30000
χ252222222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2-222-1-1-1-11111000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000i3−i3i3−i30000
χ262222222222-1-2-2-1-1-1-1-1-1-1-2-222-2-2-2-2-222-1-1-1-11111000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000−i3i3−i3i30000
χ2722222-2-22-2-2222222222222-2-2-2-2-2-2222-2-2-2-22222000022-2-2-2-2-2-2220000000000000000000000000000000000
χ2822222-2-22-2-22222222222-2-22222-2-22-2-2-2-2-2-222220000-2-22222-2-2-2-20000000000000000000000000000000000
χ2922222-2-22-2-2-122-1-1-1-1-1-1-122-2-2-2-2-2-22221111-1-1-1-10000-1-1111111-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000−i3i3i3−i30000
χ3022222-2-22-2-2-122-1-1-1-1-1-1-122-2-2-2-2-2-22221111-1-1-1-10000-1-1111111-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000i3−i3−i3i30000
χ3122222-2-22-2-2-122-1-1-1-1-1-1-1-2-22222-2-22-2-21111-1-1-1-1000011-1-1-1-11111−i3−i3i3i3i3i3−i3−i3000000000000000000i3−i3−i3i30000
χ3222222-2-22-2-2-122-1-1-1-1-1-1-1-2-22222-2-22-2-21111-1-1-1-1000011-1-1-1-11111i3i3−i3−i3−i3−i3i3i3000000000000000000−i3i3i3−i30000
χ3322222-2-22-2-2-1-2-2-1-1-1-1-1-1-12222-2-222-2-2-21111111122-2-2-1-1-1-111-1-111-1-1-1-1111100000000000000002-2-1-1110000
χ3422222-2-22-2-2-1-2-2-1-1-1-1-1-1-12222-2-222-2-2-211111111-2-222-1-1-1-111-1-1111111-1-1-1-10000000000000000-2211-1-10000
χ3522222-2-22-2-2-1-2-2-1-1-1-1-1-1-1-2-2-2-22222-2221111111122-2-21111-1-1-1-1-1-1-1-1-1-111110000000000000000-2211-1-10000
χ3622222-2-22-2-2-1-2-2-1-1-1-1-1-1-1-2-2-2-22222-22211111111-2-2221111-1-1-1-1-1-11111-1-1-1-100000000000000002-2-1-1110000
χ372222-22-2-22-2222-2-222-2-220000002-2-20022-2-222-2-200000000002-200000000000000000022-2-222-2-20000000000
χ382222-22-2-22-2222-2-222-2-220000002-2-20022-2-222-2-200000000002-2000000000000000000-2-222-2-2220000000000
χ392222-22-2-22-22-2-2-2-222-2-22000000-2220022-2-2-2-2220000000000-2200000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ402222-22-2-22-22-2-2-2-222-2-22000000-2220022-2-2-2-2220000000000-220000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ412222-2-22-2-22222-2-222-2-22000000-22-200-2-22222-2-20000000000-22000000000022-2-2-2-222000000000000000000
χ422222-2-22-2-22222-2-222-2-22000000-22-200-2-22222-2-20000000000-220000000000-2-22222-2-2000000000000000000
χ432222-2-22-2-222-2-2-2-222-2-220000002-2200-2-222-2-22200000000002-20000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ442222-2-22-2-222-2-2-2-222-2-220000002-2200-2-222-2-22200000000002-2000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ4522-2-2222-2-2-2200222-2-2-2-22-2002-2000002-22-2000000002-2002-20000000000002−22−22−22−22−22−22−22−20000000000
χ4622-2-2222-2-2-2200222-2-2-2-22-2002-2000002-22-2000000002-2002-2000000000000−22−22−22−22−22−22−22−220000000000
χ4722-2-2222-2-2-2200222-2-2-2-2-2200-22000002-22-200000000-2200-220000000000002−22−22−22−2−22−22−22−220000000000
χ4822-2-2222-2-2-2200222-2-2-2-2-2200-22000002-22-200000000-2200-22000000000000−22−22−22−222−22−22−22−20000000000
χ4922-2-22-2-2-222200222-2-2-2-22-200-2200000-22-22000000002-200-22000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000
χ5022-2-22-2-2-222200222-2-2-2-22-200-2200000-22-22000000002-200-22000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000
χ5122-2-22-2-2-222200222-2-2-2-2-22002-200000-22-2200000000-22002-2000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ5222-2-22-2-2-222200222-2-2-2-2-22002-200000-22-2200000000-22002-2000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ5322-2-2-22-22-22200-2-22-222-2002i−2i000002i−2i2-2-2200000000002i−2i00002i−2i00000000−i2i2i2−i2−i2i2i2−i22−2−222−2−220000000000
χ5422-2-2-22-22-22200-2-22-222-2002i−2i000002i−2i2-2-2200000000002i−2i00002i−2i00000000i2−i2−i2i2i2−i2−i2i2−222−2−222−20000000000
χ5522-2-2-22-22-22200-2-22-222-200−2i2i00000−2i2i2-2-220000000000−2i2i0000−2i2i00000000−i2i2i2−i2−i2i2i2−i2−222−2−222−20000000000
χ5622-2-2-22-22-22200-2-22-222-200−2i2i00000−2i2i2-2-220000000000−2i2i0000−2i2i00000000i2−i2−i2i2i2−i2−i2i22−2−222−2−220000000000
χ5722-2-2-2-2222-2200-2-22-222-2002i−2i00000−2i2i-222-200000000002i−2i0000−2i2i000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ5822-2-2-2-2222-2200-2-22-222-2002i−2i00000−2i2i-222-200000000002i−2i0000−2i2i00000000−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ5922-2-2-2-2222-2200-2-22-222-200−2i2i000002i−2i-222-20000000000−2i2i00002i−2i000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ6022-2-2-2-2222-2200-2-22-222-200−2i2i000002i−2i-222-20000000000−2i2i00002i−2i00000000−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ614444-44-4-44-4-24422-2-222-20000004-4-400-2-222-2-2220000000000-22000000000000000000000000000000000000
χ624444-44-4-44-4-2-4-422-2-222-2000000-44400-2-22222-2-200000000002-2000000000000000000000000000000000000
χ634444-4-44-4-44-24422-2-222-2000000-44-40022-2-2-2-22200000000002-2000000000000000000000000000000000000
χ644444-4-44-4-44-2-4-422-2-222-20000004-440022-2-222-2-20000000000-22000000000000000000000000000000000000
χ6544-4-4444-4-4-4-200-2-2-222224-4004-400000-22-2200000000-2200-2200000000000000000000000000000000000000
χ6644-4-4444-4-4-4-200-2-2-22222-4400-4400000-22-22000000002-2002-200000000000000000000000000000000000000
χ6744-4-44-4-4-444-200-2-2-222224-400-44000002-22-200000000-22002-200000000000000000000000000000000000000
χ6844-4-44-4-4-444-200-2-2-22222-44004-4000002-22-2000000002-200-2200000000000000000000000000000000000000
χ6944-4-4-44-44-44-20022-22-2-22004i−4i000004i−4i-222-20000000000−2i2i0000−2i2i0000000000000000000000000000000000
χ7044-4-4-44-44-44-20022-22-2-2200−4i4i00000−4i4i-222-200000000002i−2i00002i−2i0000000000000000000000000000000000
χ7144-4-4-4-4444-4-20022-22-2-22004i−4i00000−4i4i2-2-220000000000−2i2i00002i−2i0000000000000000000000000000000000
χ7244-4-4-4-4444-4-20022-22-2-2200−4i4i000004i−4i2-2-2200000000002i−2i0000−2i2i0000000000000000000000000000000000
χ734-4-4400000044-400-4-40040000000000000004-4002-22-200000000002-22-22-22-200000000000000000000000000
χ744-4-4400000044-400-4-40040000000000000004-400-22-220000000000-22-22-22-2200000000000000000000000000
χ754-4-440000004-4400-4-4004000000000000000-44002-2-2200000000002-22-2-22-2200000000000000000000000000
χ764-4-440000004-4400-4-4004000000000000000-4400-222-20000000000-22-222-22-200000000000000000000000000
χ774-4-44000000-24-4−2i32i322−2i32i3-2000000000000000-22−2i32i32-22-20000000000−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ784-4-44000000-24-4−2i32i322−2i32i3-2000000000000000-22−2i32i3-22-2200000000001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ794-4-44000000-24-42i3−2i3222i3−2i3-2000000000000000-222i3−2i32-22-20000000000−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ804-4-44000000-24-42i3−2i3222i3−2i3-2000000000000000-222i3−2i3-22-2200000000001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ814-4-44000000-2-44−2i32i322−2i32i3-20000000000000002-22i3−2i32-2-220000000000−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ824-4-44000000-2-44−2i32i322−2i32i3-20000000000000002-22i3−2i3-222-200000000001+i3−1−i31−i3−1+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ834-4-44000000-2-442i3−2i3222i3−2i3-20000000000000002-2−2i32i32-2-220000000000−1+i31−i3−1−i31+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ844-4-44000000-2-442i3−2i3222i3−2i3-20000000000000002-2−2i32i3-222-200000000001−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ858-88-800000080000-8800-80000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-400−4i34i34-44i3−4i340000000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-4004i3−4i34-4−4i34i340000000000000000000000000000000000000000000000000000000000000000000

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