Finite Group Databasebeta

← Group #10772156

Character table — Group #10772156

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888888888888888121212121616161624242424242448484848
order1222344444466612121212244466121212121212244488888888121224242424242424242424242424242424444461212122224444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-111-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-11-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-1
χ9111111-1-11111111111-1-1-11-1-111-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1111-1-11-11-1
χ10111111-1-11111111111-1-1-11-1-111-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-111-11-11
χ11111111-1-11111111111-1-1-11-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1111-1-1-11-11
χ12111111-1-11111111111-1-1-11-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1-1-1111-11-1
χ13111111-1-11111111111-1-1-11-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11111-1-11
χ14111111-1-11111111111-1-1-11-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111111-1-1-1-111-1
χ15111111-1-11111111111-1-1-11-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1111-111-1
χ16111111-1-11111111111-1-1-11-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111111-1-1-11-1-11
χ1722222222-22-222222222-2-2-222-2-222-2-2000000000000-2-2000000000000000022-2-20000200-2000000
χ1822222222-22-222222222-2-2-222-2-222-2-2000000000000-2-20000000000000000-2-2220000-2002000000
χ19222222-2-2-22-22222222-222-2-2-2-2-2-2-2-2-200000000000022000000000000000022220000-200-2000000
χ20222222-2-2-22-22222222-222-2-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2-2-200002002000000
χ2122222-2222-22222-2-2-2-2-22-2-2-2-22222-2-22-2-22000000002-2000000000000000000002-22-20000000000
χ2222222-2222-22222-2-2-2-2-22-2-2-2-22222-2-2-222-2000000002-200000000000000000000-22-220000000000
χ2322222-222-2-2-2222-2-2-2-2-2-222-2-2-2-22222000000000000-2200000000000000000000000002-202-20000
χ2422222-222-2-2-2222-2-2-2-2-2-222-2-2-2-22222000000000000-220000000000000000000000000-220-220000
χ2522222-2-2-22-22222-2-2-2-22-22-22222-2-2-2-22-22-200000000-22000000000000000000002-2-220000000000
χ2622222-2-2-22-22222-2-2-2-22-22-22222-2-2-2-2-22-2200000000-2200000000000000000000-222-20000000000
χ2722222-2-2-2-2-2-2222-2-2-2-222-2222-2-2-2-2220000000000002-200000000000000000000000002-20-220000
χ2822222-2-2-2-2-2-2222-2-2-2-222-2222-2-2-2-2220000000000002-20000000000000000000000000-2202-20000
χ292222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-10000000000
χ302222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000-1-1-1-10000000000
χ312222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000011110000000000
χ322222-1222222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000011110000000000
χ332222-12-2-2222-1-1-1-1-1-1-1-2-2-2211-1-111-1-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-111110000-1-1110000000000
χ342222-12-2-2222-1-1-1-1-1-1-1-2-2-2211-1-111-1-122-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-10000-1-1110000000000
χ352222-12-2-2222-1-1-1-1-1-1-1-2-2-2211-1-111-1-1-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-1000011-1-10000000000
χ362222-12-2-2222-1-1-1-1-1-1-1-2-2-2211-1-111-1-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-11111000011-1-10000000000
χ372222-1-2222-22-1-1-11111-22-2-211-1-1-1-1112-2-2200000000-1133−3−333−3−333−3−333−3−30000-11-110000000000
χ382222-1-2222-22-1-1-11111-22-2-211-1-1-1-1112-2-2200000000-11−3−333−3−333−3−333−3−3330000-11-110000000000
χ392222-1-2222-22-1-1-11111-22-2-211-1-1-1-111-222-200000000-1133−3−333−3−3−3−333−3−33300001-11-10000000000
χ402222-1-2222-22-1-1-11111-22-2-211-1-1-1-111-222-200000000-11−3−333−3−33333−3−333−3−300001-11-10000000000
χ412222-1-2-2-22-22-1-1-111112-22-2-1-1-1-111112-22-2000000001-133−3−3−3−33333−3−3−3−3330000-111-10000000000
χ422222-1-2-2-22-22-1-1-111112-22-2-1-1-1-111112-22-2000000001-1−3−33333−3−3−3−33333−3−30000-111-10000000000
χ432222-1-2-2-22-22-1-1-111112-22-2-1-1-1-11111-22-22000000001-133−3−3−3−333−3−33333−3−300001-1-110000000000
χ442222-1-2-2-22-22-1-1-111112-22-2-1-1-1-11111-22-22000000001-1−3−33333−3−333−3−3−3−33300001-1-110000000000
χ454444-2444-44-4-2-2-2-2-2-2-24-4-4-4-2-222-2-222000000000000220000000000000000000000000000000000
χ464444-24-4-4-44-4-2-2-2-2-2-2-2-444-422222222000000000000-2-20000000000000000000000000000000000
χ474444-2-444-4-4-4-2-2-22222-4-4442222-2-2-2-20000000000002-20000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2222244-44-2-22222-2-2000000000000-220000000000000000000000000000000000
χ4944-4-444000-404-4-444-4-40000000000000000000000000000000000000000004-40000000000000000
χ5044-4-444000-404-4-444-4-4000000000000000000000000000000000000000000-440000000000000000
χ5144-4-44-4000404-4-4-4-444000000000000000000000000000000000000000000004i−4i00000000000000
χ5244-4-44-4000404-4-4-4-44400000000000000000000000000000000000000000000−4i4i00000000000000
χ534-44-4404i−4i000-44-40000000000004i−4i00000000002-22i−2i00000000002-22-22i−2i2i−2i000000000000000000
χ544-44-4404i−4i000-44-40000000000004i−4i0000000000-22−2i2i0000000000-22-22−2i2i−2i2i000000000000000000
χ554-44-440−4i4i000-44-4000000000000−4i4i00000000002-2−2i2i00000000002-22-2−2i2i−2i2i000000000000000000
χ564-44-440−4i4i000-44-4000000000000−4i4i0000000000-222i−2i0000000000-22-222i−2i2i−2i000000000000000000
χ574-44-4-204i−4i0002-2223−2323−230000−2i32i300−2i2i00000000002-22i−2i0000000000−1−31+3−1+31−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000
χ584-44-4-204i−4i0002-2223−2323−230000−2i32i300−2i2i0000000000-22−2i2i00000000001+3−1−31−3−1+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000
χ594-44-4-204i−4i0002-22−2323−232300002i3−2i300−2i2i00000000002-22i−2i0000000000−1+31−3−1−31+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000
χ604-44-4-204i−4i0002-22−2323−232300002i3−2i300−2i2i0000000000-22−2i2i00000000001−3−1+31+3−1−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000
χ614-44-4-20−4i4i0002-2223−2323−2300002i3−2i3002i−2i00000000002-2−2i2i0000000000−1−31+3−1+31−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000
χ624-44-4-20−4i4i0002-2223−2323−2300002i3−2i3002i−2i0000000000-222i−2i00000000001+3−1−31−3−1+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000
χ634-44-4-20−4i4i0002-22−2323−23230000−2i32i3002i−2i00000000002-2−2i2i0000000000−1+31−3−1−31+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000
χ644-44-4-20−4i4i0002-22−2323−23230000−2i32i3002i−2i0000000000-222i−2i00000000001−3−1+31+3−1−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000
χ654-4-44400040-4-4-4400000000004-40000000000−2i22i20000000000−2i22i2−2i22i200000000000000000000000000
χ664-4-44400040-4-4-4400000000004-400000000002i2−2i200000000002i2−2i22i2−2i200000000000000000000000000
χ674-4-444000-404-4-440000000000-440000000022−220000000022−2222−22000000000000000000000000000000
χ684-4-444000-404-4-440000000000-4400000000−222200000000−2222−2222000000000000000000000000000000
χ694-4-44-200040-422-223−23−2323000000-220023−23000000−2i22i200000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ704-4-44-200040-422-223−23−2323000000-220023−230000002i2−2i20000000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ714-4-44-200040-422-2−232323−23000000-2200−2323000000−2i22i200000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ724-4-44-200040-422-2−232323−23000000-2200−23230000002i2−2i20000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ734-4-44-2000-40422-223−23−23230000002-200−2323000022−22000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000
χ744-4-44-2000-40422-223−23−23230000002-200−23230000−222200000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000
χ754-4-44-2000-40422-2−232323−230000002-20023−23000022−22000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000
χ764-4-44-2000-40422-2−232323−230000002-20023−230000−222200000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ7788-8-8-48000-80-444-4-444000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4-800080-44444-4-4000000000000000000000000000000000000000000000000000000000000

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