Finite Group Databasebeta

← Group #10692290

Character table — Group #10692290

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order1222344444466612121212222444441212121212121212446668888121212121212122424242424242424888888242424248888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-11-1-11111111111-1-11-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ61111111111111111111-1-11-1-11111111111-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111-1-11-1-11111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111-1-11-1-11111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ911111-11-1-11-1111-1-1-1-1111-1-1-11-11111-1-1-1-1-11111ii−i−i-111-1-1-1-1iiii−i−i−i−iii−i−ii−iii−i−ii−iii−i−i1-11-1
χ1011111-11-1-11-1111-1-1-1-1111-1-1-11-11111-1-1-1-1-11111ii−i−i-111-1-1-1-1iiii−i−i−i−i−i−iiii−iii−i−i−ii−i−iii-11-11
χ1111111-11-1-11-1111-1-1-1-1111-1-1-11-11111-1-1-1-1-11111−i−iii-111-1-1-1-1−i−i−i−iiiiiii−i−i−ii−i−iiii−iii−i−i-11-11
χ1211111-11-1-11-1111-1-1-1-1111-1-1-11-11111-1-1-1-1-11111−i−iii-111-1-1-1-1−i−i−i−iiiii−i−iii−ii−i−iii−ii−i−iii1-11-1
χ1311111-11-1-11-1111-1-1-1-11-1-1-1111-11111-1-1-1-11-11-1-1ii−i−i-1-1-11111iiii−i−i−i−iii−i−i−ii−i−iiii−i−i−iii-111-1
χ1411111-11-1-11-1111-1-1-1-11-1-1-1111-11111-1-1-1-11-11-1-1ii−i−i-1-1-11111iiii−i−i−i−i−i−iii−ii−i−iii−iiii−i−i1-1-11
χ1511111-11-1-11-1111-1-1-1-11-1-1-1111-11111-1-1-1-11-11-1-1−i−iii-1-1-11111−i−i−i−iiiiiii−i−ii−iii−i−ii−i−i−iii1-1-11
χ1611111-11-1-11-1111-1-1-1-11-1-1-1111-11111-1-1-1-11-11-1-1−i−iii-1-1-11111−i−i−i−iiiii−i−iiii−iii−i−i−iiii−i−i-111-1
χ1722222222-22-22222222-222-2-2-2-2222-2-2-2-2222-2-2220000-2-2-222-2-20000000000000000000000000000
χ1822222222-22-22222222-2-2-2-222-2222-2-2-2-222-22-2-2-20000-222-2-2220000000000000000000000000000
χ19222222-222-222222222-200-2002-2-2-22222-2-200-2000000-2000000000000002222000000-2-200000000
χ20222222-222-222222222-200-2002-2-2-22222-2-200-2000000-200000000000000-2-2-2-20000002200000000
χ21222222-22-2-2-22222222200200-2-2-2-2-2-2-2-2-2-20020000002000000000000000000000000002i−2i2i−2i0000
χ22222222-22-2-2-22222222200200-2-2-2-2-2-2-2-2-2-2002000000200000000000000000000000000−2i2i−2i2i0000
χ2322222-22-2222222-2-2-2-2-222222-2-222-2-222-2-2-2-2-22200002-2-2-2-2220000000000000000000000000000
χ2422222-22-2222222-2-2-2-2-2-2-22-2-2-2-222-2-222-2-222-2-2-2000022222-2-20000000000000000000000000000
χ2522222-2-2-22-22222-2-2-2-2200-200-22-2-2-2-22222002000000-2000000000000000000000000002-2-220000
χ2622222-2-2-22-22222-2-2-2-2200-200-22-2-2-2-22222002000000-200000000000000000000000000-222-20000
χ2722222-2-2-2-2-2-2222-2-2-2-2-20020022-2-222-2-22200-20000002000000000000002i2i−2i−2i000000−2i2i00000000
χ2822222-2-2-2-2-2-2222-2-2-2-2-20020022-2-222-2-22200-2000000200000000000000−2i−2i2i2i0000002i−2i00000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1111111110000-2-211110000000000
χ312222-1222222-1-1-1-1-1-1-12-2-22-2-222-1-1-1-1-1-1-1-1-2-2-1112222-1111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ322222-1222222-1-1-1-1-1-1-12-2-22-2-222-1-1-1-1-1-1-1-1-2-2-111-2-2-2-2-111111111111111000022-1-1-1-10000000000
χ332222-1222-22-2-1-1-1-1-1-1-1-222-2-2-2-22-1-11111-1-12-21-1-10000111-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i30000000000
χ342222-1222-22-2-1-1-1-1-1-1-1-222-2-2-2-22-1-11111-1-12-21-1-10000111-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i30000000000
χ352222-1222-22-2-1-1-1-1-1-1-1-2-2-2-222-22-1-11111-1-1-2211100001-1-111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i30000000000
χ362222-1222-22-2-1-1-1-1-1-1-1-2-2-2-222-22-1-11111-1-1-2211100001-1-111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i30000000000
χ372222-1-22-2222-1-1-11111-222222-2-2-1-111-1-111-2-21-1-10000-11111-1-133−3−3−3−3330000003−3−330000000000
χ382222-1-22-2222-1-1-11111-222222-2-2-1-111-1-111-2-21-1-10000-11111-1-1−3−33333−3−3000000−333−30000000000
χ392222-1-22-2222-1-1-11111-2-2-22-2-2-2-2-1-111-1-111221110000-1-1-1-1-11133−3−3−3−333000000−333−30000000000
χ402222-1-22-2222-1-1-11111-2-2-22-2-2-2-2-1-111-1-111221110000-1-1-1-1-111−3−33333−3−30000003−3−330000000000
χ412222-1-22-2-22-2-1-1-11111222-2-2-22-2-1-1-1-11111-22-1-1-12i2i−2i−2i1-1-11111−i−i−i−iiiii00002i−2i−i−iii0000000000
χ422222-1-22-2-22-2-1-1-11111222-2-2-22-2-1-1-1-11111-22-1-1-1−2i−2i2i2i1-1-11111iiii−i−i−i−i0000−2i2iii−i−i0000000000
χ432222-1-22-2-22-2-1-1-111112-2-2-2222-2-1-1-1-111112-2-1112i2i−2i−2i111-1-1-1-1−i−i−i−iiiii0000−2i2iii−i−i0000000000
χ442222-1-22-2-22-2-1-1-111112-2-2-2222-2-1-1-1-111112-2-111−2i−2i2i2i111-1-1-1-1iiii−i−i−i−i00002i−2i−i−iii0000000000
χ454444-24-444-44-2-2-2-2-2-2-2-400-4004-422-2-2-2-22200200000020000000000000000000000000000000000
χ464444-24-44-4-4-4-2-2-2-2-2-2-2400400-4-42222222200-2000000-20000000000000000000000000000000000
χ474444-2-4-4-44-44-2-2-22222400-400-442222-2-2-2-200-200000020000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-22222-4004004422-2-222-2-2002000000-20000000000000000000000000000000000
χ4944-4-4400040-44-4-400000000000000004-400000002-22-200000002-22-22-22-200000000000000000000
χ5044-4-4400040-44-4-400000000000000004-40000000-22-220000000-22-22-22-2200000000000000000000
χ5144-4-44000-4044-4-40000000000000000-4400000002i−2i−2i2i00000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ5244-4-44000-4044-4-40000000000000000-440000000−2i2i2i−2i0000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ5344-4-4-200040-4-22223−2323−23000000000023−23-2200000002-22-20000000−1+31−3−1−31+3−1−31+3−1+31−300000000000000000000
χ5444-4-4-200040-4-22223−2323−23000000000023−23-220000000-22-2200000001−3−1+31+3−1−31+3−1−31−3−1+300000000000000000000
χ5544-4-4-200040-4-222−2323−23230000000000−2323-2200000002-22-20000000−1−31+3−1+31−3−1+31−3−1−31+300000000000000000000
χ5644-4-4-200040-4-222−2323−23230000000000−2323-220000000-22-2200000001+3−1−31−3−1+31−3−1+31+3−1−300000000000000000000
χ5744-4-4-2000-404-22223−2323−230000000000−23232-200000002i−2i−2i2i0000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ5844-4-4-2000-404-22223−2323−230000000000−23232-20000000−2i2i2i−2i0000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ5944-4-4-2000-404-222−2323−2323000000000023−232-200000002i−2i−2i2i0000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ6044-4-4-2000-404-222−2323−2323000000000023−232-20000000−2i2i2i−2i0000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ614-44-4440-4000-44-444-4-4000000000000000000000000000000000000000022−2222−220000000000000000
χ624-44-4440-4000-44-444-4-40000000000000000000000000000000000000000−2222−22220000000000000000
χ634-44-44-404000-44-4-4-4440000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ644-44-44-404000-44-4-4-44400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ654-4-4440400-40-4-44000000004i−4i004-4000000000000000000004i−4i0000000000000000000000000000
χ664-4-4440400-40-4-4400000000−4i4i004-400000000000000000000−4i4i0000000000000000000000000000
χ674-4-4440-40040-4-44000004-400000-440000000004-4000000000000000000000000000000000000000
χ684-4-4440-40040-4-4400000-4400000-44000000000-44000000000000000000000000000000000000000
χ694-4-44-20400-4022-223−23−232300004i−4i00-22000023−230000000000−2i32i300−2i2i0000000000000000000000000000
χ704-4-44-20400-4022-223−23−23230000−4i4i00-22000023−2300000000002i3−2i3002i−2i0000000000000000000000000000
χ714-4-44-20400-4022-2−232323−2300004i−4i00-220000−232300000000002i3−2i300−2i2i0000000000000000000000000000
χ724-4-44-20400-4022-2−232323−230000−4i4i00-220000−23230000000000−2i32i3002i−2i0000000000000000000000000000
χ734-4-44-20-4004022-223−23−232304-4000002-20000−2323000-22000000023−23000000000000000000000000000000
χ744-4-44-20-4004022-223−23−23230-44000002-20000−23230002-20000000−2323000000000000000000000000000000
χ754-4-44-20-4004022-2−232323−2304-4000002-2000023−23000-220000000−2323000000000000000000000000000000
χ764-4-44-20-4004022-2−232323−230-44000002-2000023−230002-2000000023−23000000000000000000000000000000
χ778-88-8-480-80004-44-4-444000000000000000000000000000000000000000000000000000000000000
χ788-88-8-4-8080004-4444-4-4000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.