Finite Group Databasebeta

← Group #10692360

Character table — Group #10692360

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order12222234444666121212122244444466661212121244444461212121212121212121212121212121212444488242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ91111-1-11-1-111111-1-1-1-11-11-111-1-1-1-1-1-111111-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−iii−i−ii−iii−i−ii−iii−i−i1-11-1
χ101111-1-11-1-111111-1-1-1-11-11-111-1-1-1-1-1-111111-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−iiii−iii−i−i−ii−i−iii-11-11
χ111111-1-11-1-111111-1-1-1-11-11-111-1-1-1-1-1-111111-1−i−iii1-11111-1-1-1-1−i−i−i−iiiiiii−i−i−ii−i−iiii−iii−i−i-11-11
χ121111-1-11-1-111111-1-1-1-11-11-111-1-1-1-1-1-111111-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−iii−ii−i−iii−ii−i−iii1-11-1
χ131111-1-11-1-111111-1-1-1-11-11-1-1-111-1-1-1-11111-11ii−i−i1-1-1-1-1-11111iiii−i−i−i−iii−i−i−ii−i−iiii−i−i−iii-111-1
χ141111-1-11-1-111111-1-1-1-11-11-1-1-111-1-1-1-11111-11ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−iii−ii−i−iii−iiii−i−i1-1-11
χ151111-1-11-1-111111-1-1-1-11-11-1-1-111-1-1-1-11111-11−i−iii1-1-1-1-1-11111−i−i−i−iiiiiii−i−ii−iii−i−ii−i−i−iii1-1-11
χ161111-1-11-1-111111-1-1-1-11-11-1-1-111-1-1-1-11111-11−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−iiii−iii−i−i−iiii−i−i-111-1
χ17222222222-2-22222222-2-22-2000022-2-222-2-2000000-2-200000000000000002222000000-2-200000000
χ18222222222-2-22222222-2-22-2000022-2-222-2-2000000-2-20000000000000000-2-2-2-20000002200000000
χ192222222-2-222222-2-2-2-2-2-2-22222222-2-2-2-222-2-20000-2222-2-222-2-20000000000000000000000000000
χ202222222-2-222222-2-2-2-2-2-2-22-2-2-2-222-2-2-2-222220000-22-2-222-2-2220000000000000000000000000000
χ212222222-2-2-2-2222-2-2-2-222-2-200002222-2-2-2-20000002-200000000000000000000000000002-22-20000
χ222222222-2-2-2-2222-2-2-2-222-2-200002222-2-2-2-20000002-20000000000000000000000000000-22-220000
χ23222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ24222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-211110000000000
χ25222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ26222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-10000000000
χ27222222-1-2-222-1-1-11111-2-2-222222-1-11111-1-1-2-200001-1-1-111-1-11133−3−333−3−30000003−33−30000000000
χ28222222-1-2-222-1-1-11111-2-2-222222-1-11111-1-1-2-200001-1-1-111-1-111−3−333−3−333000000−33−330000000000
χ29222222-1-2-222-1-1-11111-2-2-22-2-2-2-2-1-11111-1-12200001-111-1-111-1-133−3−333−3−3000000−33−330000000000
χ30222222-1-2-222-1-1-11111-2-2-22-2-2-2-2-1-11111-1-12200001-111-1-111-1-1−3−333−3−3330000003−33−30000000000
χ312222-2-2222222222222-22-2-222-2-2-2-222-2-222-220000-2-222-2-2-2-2220000000000000000000000000000
χ322222-2-2222222222222-22-2-2-2-222-2-222-2-2222-20000-2-2-2-22222-2-20000000000000000000000000000
χ332222-2-2222-2-222222222-2-220000-2-2-2-2-2-2-2-20000002200000000000000000000000000002i−2i−2i2i0000
χ342222-2-2222-2-222222222-2-220000-2-2-2-2-2-2-2-2000000220000000000000000000000000000−2i2i2i−2i0000
χ352222-2-22-2-2-2-2222-2-2-2-2-22220000-2-22222-2-2000000-2200000000000000002i2i−2i−2i000000−2i2i00000000
χ362222-2-22-2-2-2-2222-2-2-2-2-22220000-2-22222-2-2000000-220000000000000000−2i−2i2i2i0000002i−2i00000000
χ372222-2-2-12222-1-1-1-1-1-1-1-22-2-222-2-211-1-111-1-1-22000011-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i30000000000
χ382222-2-2-12222-1-1-1-1-1-1-1-22-2-222-2-211-1-111-1-1-22000011-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i30000000000
χ392222-2-2-12222-1-1-1-1-1-1-1-22-2-2-2-22211-1-111-1-12-200001111-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i30000000000
χ402222-2-2-12222-1-1-1-1-1-1-1-22-2-2-2-22211-1-111-1-12-200001111-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i30000000000
χ412222-2-2-1-2-222-1-1-111112-22-222-2-21111-1-1-1-12-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii00002i−2i−i−iii0000000000
χ422222-2-2-1-2-222-1-1-111112-22-222-2-21111-1-1-1-12-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i0000−2i2iii−i−i0000000000
χ432222-2-2-1-2-222-1-1-111112-22-2-2-2221111-1-1-1-1-222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii0000−2i2iii−i−i0000000000
χ442222-2-2-1-2-222-1-1-111112-22-2-2-2221111-1-1-1-1-22−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i00002i−2i−i−iii0000000000
χ45444444-244-4-4-2-2-2-2-2-2-2-4-44-40000-2-222-2-22200000022000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2222244-4-40000-2-2-2-22222000000-22000000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-2-2-2-24-4-44000022222222000000-2-2000000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-22222-4444000022-2-2-2-2220000002-2000000000000000000000000000000000000
χ4944-4-44-4400004-4-40000000000004-4000000002-22-200000000002-22-22-22-200000000000000000000
χ5044-4-44-4400004-4-40000000000004-400000000-22-220000000000-22-22-22-2200000000000000000000
χ5144-4-44-4-20000-2222323−23−2300000000-220023−2300002-22-20000000000−1+31−3−1−31+3−1+31−3−1−31+300000000000000000000
χ5244-4-44-4-20000-2222323−23−2300000000-220023−230000-22-2200000000001−3−1+31+3−1−31−3−1+31+3−1−300000000000000000000
χ5344-4-44-4-20000-222−23−23232300000000-2200−232300002-22-20000000000−1−31+3−1+31−3−1−31+3−1+31−300000000000000000000
χ5444-4-44-4-20000-222−23−23232300000000-2200−23230000-22-2200000000001+3−1−31−3−1+31+3−1−31−3−1+300000000000000000000
χ5544-4-4-44400004-4-4000000000000-44000000002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ5644-4-4-44400004-4-4000000000000-4400000000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ5744-4-4-44-20000-2222323−23−23000000002-200−232300002i−2i−2i2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000
χ5844-4-4-44-20000-2222323−23−23000000002-200−23230000−2i2i2i−2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000
χ5944-4-4-44-20000-222−23−232323000000002-20023−2300002i−2i−2i2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000
χ6044-4-4-44-20000-222−23−232323000000002-20023−230000−2i2i2i−2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000
χ614-44-4004004-4-44-400000000004i−4i0000004-40000000000004i−4i000000000000000000000000000000
χ624-44-4004004-4-44-40000000000−4i4i0000004-4000000000000−4i4i000000000000000000000000000000
χ634-44-400400-44-44-4000000004i−4i00000000-44000000004i−4i0000000000000000000000000000000000
χ644-44-400400-44-44-400000000−4i4i00000000-4400000000−4i4i0000000000000000000000000000000000
χ654-44-400-2004-42-22−2i32i3−2i32i30000004i−4i00−2i32i300-22000000000023−23−2i2i000000000000000000000000000000
χ664-44-400-2004-42-22−2i32i3−2i32i3000000−4i4i00−2i32i300-220000000000−23232i−2i000000000000000000000000000000
χ674-44-400-2004-42-222i3−2i32i3−2i30000004i−4i002i3−2i300-220000000000−2323−2i2i000000000000000000000000000000
χ684-44-400-2004-42-222i3−2i32i3−2i3000000−4i4i002i3−2i300-22000000000023−232i−2i000000000000000000000000000000
χ694-44-400-200-442-22−2i32i3−2i32i300004i−4i00002i3−2i3002-200000000−2i2i000023−230000000000000000000000000000
χ704-44-400-200-442-22−2i32i3−2i32i30000−4i4i00002i3−2i3002-2000000002i−2i0000−23230000000000000000000000000000
χ714-44-400-200-442-222i3−2i32i3−2i300004i−4i0000−2i32i3002-200000000−2i2i0000−23230000000000000000000000000000
χ724-44-400-200-442-222i3−2i32i3−2i30000−4i4i0000−2i32i3002-2000000002i−2i000023−230000000000000000000000000000
χ734-4-440044i−4i00-4-444i−4i−4i4i00000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000
χ744-4-440044i−4i00-4-444i−4i−4i4i0000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000
χ754-4-44004−4i4i00-4-44−4i4i4i−4i00000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000
χ764-4-44004−4i4i00-4-44−4i4i4i−4i0000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000
χ778-8-8800-48i−8i0044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ788-8-8800-4−8i8i0044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.