Finite Group Databasebeta

← Group #10691482

Character table — Group #10691482

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12224444223444444666121212124466121212121212224466668888121212121212242424242424242444444444246612124444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-111111-11-111-1-111-1-11-111-1-11111-1-1-1-1ii−i−iii−i−i1-111-1-1ii−i−iii−i−ii−i
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-111111-11-111-1-111-1-11-111-1-11111-1-1-1-1−i−iii−i−iii1-111-1-1−i−iii−i−iii−ii
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-111111-11-111-1-1-1-1111-111-1-1-1-1-1-11111ii−i−iii−i−i-11-1-111ii−i−i−i−iii−ii
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-111111-11-111-1-1-1-1111-111-1-1-1-1-1-11111−i−iii−i−iii-11-1-111−i−iiiii−i−ii−i
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-11111-11-11-1-11111-1-11-1-1-1111111-1-1-1-1ii−i−iii−i−i-11-1-111−i−iiiii−i−i−ii
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-11111-11-11-1-11111-1-11-1-1-1111111-1-1-1-1−i−iii−i−iii-11-1-111ii−i−i−i−iiii−i
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-11111-11-11-1-111-1-1111-1-1-111-1-1-1-11111ii−i−iii−i−i1-111-1-1−i−iii−i−iiii−i
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1-1-11111-11-11-1-111-1-1111-1-1-111-1-1-1-11111−i−iii−i−iii1-111-1-1ii−i−iii−i−i−ii
χ172222222222222-2-2-2-22222222-2-222-2-222-2-2000000000000-2-20000000000002222-2-2-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-222-2-222-2-2000000000000-2-2000000000000-2-2-2-222220000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-11111111111110000000022-1-1-1-10000000000
χ2322222222-2-22-2-222222222222-2-2-2-222-2-2222-2-2222-2-20000-2-2-2-22200000000000000000000000000000000
χ2422222222-2-22-2-222222222222-2-2-2-222-2-222-222-2-2-2220000-2-222-2-200000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000000000000002i−2i2i−2i000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000−2i2i−2i2i000000
χ2722222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-211-1-111-1-12-2-22-1-11100001111-1-1−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-211-1-111-1-12-2-22-1-11100001111-1-1i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-211-1-111-1-1-222-211-1-1000011-1-111−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-211-1-111-1-1-222-211-1-1000011-1-111i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-2-2222-2-2-2-22222-2-222220000-22-2-2-2-200000000000000000000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-2-2222-2-2-2-222-2-222-2-2-2-20000-22222200000000000000000000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-22222-2-2-2-20000000000002-2000000000000000000000000002-2-22000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-22222-2-2-2-20000000000002-200000000000000000000000000-222-2000000
χ352222-2-2-2-222-1-2-222-2-2-1-1-11111-22-1-11111-1-122-2-2-1-1-1-100001-11111−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i30000000000
χ362222-2-2-2-222-1-2-222-2-2-1-1-11111-22-1-11111-1-122-2-2-1-1-1-100001-11111i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i30000000000
χ372222-2-2-2-222-1-2-222-2-2-1-1-11111-22-1-11111-1-1-2-222111100001-1-1-1-1-1−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i30000000000
χ382222-2-2-2-222-1-2-222-2-2-1-1-11111-22-1-11111-1-1-2-222111100001-1-1-1-1-1i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i30000000000
χ392222-2-2-2-2-2-2222-2-222222-2-2-2-2-22-2-22222-2-2000000000000-220000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-2222-2-222222-2-2-2-2-22-2-22222-2-2000000000000-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-2-12222-2-2-1-1-111112-21111-1-1-1-12-22-2-1-11122-2-2-11-1-111-1-1-1-11111000000002-2-1-1110000000000
χ422222-2-2-2-2-2-2-12222-2-2-1-1-111112-21111-1-1-1-12-22-2-1-111-2-222-11-1-1111111-1-1-1-100000000-2211-1-10000000000
χ432222-2-2-2-2-2-2-12222-2-2-1-1-111112-21111-1-1-1-1-22-2211-1-122-2-2-1111-1-1-1-1-1-1111100000000-2211-1-10000000000
χ442222-2-2-2-2-2-2-12222-2-2-1-1-111112-21111-1-1-1-1-22-2211-1-1-2-222-1111-1-11111-1-1-1-1000000002-2-1-1110000000000
χ452-2-2222-2-22-222-20000-2-2222-2-2002-2002-200000000002−22−20000002−22−22−22−200002i−2i2i−2i0000000000−i2i2−i2i200
χ462-2-2222-2-22-222-20000-2-2222-2-2002-2002-200000000002−22−20000002−22−22−22−20000−2i2i−2i2i0000000000i2−i2i2−i200
χ472-2-2222-2-22-222-20000-2-2222-2-2002-2002-20000000000−22−22000000−22−22−22−2200002i−2i2i−2i0000000000i2−i2i2−i200
χ482-2-2222-2-22-222-20000-2-2222-2-2002-2002-20000000000−22−22000000−22−22−22−220000−2i2i−2i2i0000000000−i2i2−i2i200
χ492-2-22-2-222-2222-20000-2-22-2-22200-22002-200000000002−2−220000002−22−2−22−2200002-2-220000000000−222−200
χ502-2-22-2-222-2222-20000-2-22-2-22200-22002-200000000002−2−220000002−22−2−22−220000-222-200000000002−2−2200
χ512-2-22-2-222-2222-20000-2-22-2-22200-22002-20000000000−222−2000000−22−222−22−200002-2-2200000000002−2−2200
χ522-2-22-2-222-2222-20000-2-22-2-22200-22002-20000000000−222−2000000−22−222−22−20000-222-20000000000−222−200
χ534444444444-244-4-4-4-4-2-2-2-2-2-2-2-4-4-2-222-2-22200000000000022000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-4-4-444-2-2-222224-4-2-2-2-22222000000000000-22000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-244-4-444-2-2-22222-4422-2-2-2-2220000000000002-2000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i0040000004-4-44i−4i4i−4i0000000000000000000000000000000000002+2i−2−2i2−2i−2+2i00000000000000000000
χ5844-4-44i−4i4i−4i0040000004-4-44i−4i4i−4i000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i00000000000000000000
χ5944-4-4−4i4i−4i4i0040000004-4-4−4i4i−4i4i0000000000000000000000000000000000002−2i−2+2i2+2i−2−2i00000000000000000000
χ6044-4-4−4i4i−4i4i0040000004-4-4−4i4i−4i4i000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i00000000000000000000
χ614-44-44i−4i−4i4i004004-44i−4i-44-44i−4i−4i4i00004i−4i004-400000000000000000000000000000000000000000000000000
χ624-44-44i−4i−4i4i00400-44−4i4i-44-44i−4i−4i4i0000−4i4i00-4400000000000000000000000000000000000000000000000000
χ634-44-44i−4i−4i4i00-2004-44i−4i2-22−2i2i2i−2i0000−2i2i00-220000−2i32i3000000000023−2300000000000000000000000000000000
χ644-44-44i−4i−4i4i00-2004-44i−4i2-22−2i2i2i−2i0000−2i2i00-2200002i3−2i30000000000−232300000000000000000000000000000000
χ654-44-44i−4i−4i4i00-200-44−4i4i2-22−2i2i2i−2i00002i−2i002-2000000−2i32i300000023−230000000000000000000000000000000000
χ664-44-44i−4i−4i4i00-200-44−4i4i2-22−2i2i2i−2i00002i−2i002-20000002i3−2i3000000−23230000000000000000000000000000000000
χ674-44-4−4i4i4i−4i004004-4−4i4i-44-4−4i4i4i−4i0000−4i4i004-400000000000000000000000000000000000000000000000000
χ684-44-4−4i4i4i−4i00400-444i−4i-44-4−4i4i4i−4i00004i−4i00-4400000000000000000000000000000000000000000000000000
χ694-44-4−4i4i4i−4i00-2004-4−4i4i2-222i−2i−2i2i00002i−2i00-220000−2i32i30000000000−232300000000000000000000000000000000
χ704-44-4−4i4i4i−4i00-2004-4−4i4i2-222i−2i−2i2i00002i−2i00-2200002i3−2i3000000000023−2300000000000000000000000000000000
χ714-44-4−4i4i4i−4i00-200-444i−4i2-222i−2i−2i2i0000−2i2i002-2000000−2i32i3000000−23230000000000000000000000000000000000
χ724-44-4−4i4i4i−4i00-200-444i−4i2-222i−2i−2i2i0000−2i2i002-20000002i3−2i300000023−230000000000000000000000000000000000
χ734-4-4444-4-44-4-24-4000022-2-2-22200-2200-22000000000022−2222−22000000−22−22−22−22000000000000000000000000
χ744-4-4444-4-44-4-24-4000022-2-2-22200-2200-220000000000−2222−22220000002−22−22−22−2000000000000000000000000
χ754-4-4444-4-4-444-440000-4-4444-4-400-4400-440000000000000000000000000000000000000000000000000000
χ764-4-4444-4-4-44-2-44000022-2-2-222002-2002-200000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ774-4-4444-4-4-44-2-44000022-2-2-222002-2002-200000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ784-4-44-4-4444-44-440000-4-44-4-444004-400-440000000000000000000000000000000000000000000000000000
χ794-4-44-4-4444-4-2-44000022-222-2-200-22002-200000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ804-4-44-4-4444-4-2-44000022-222-2-200-22002-200000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ814-4-44-4-444-44-24-4000022-222-2-2002-200-22000000000022−22−2222000000−22−222−22−2000000000000000000000000
χ824-4-44-4-444-44-24-4000022-222-2-2002-200-220000000000−222222−220000002−22−2−22−22000000000000000000000000
χ8388-8-88i−8i8i−8i00-4000000-444−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ8488-8-8−8i8i−8i8i00-4000000-4444i−4i4i−4i000000000000000000000000000000000000000000000000000000000000

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