Finite Group Databasebeta

← Group #10692771

Character table — Group #10692771

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order122234444446661212121224448888121212121212121268888881224242424242424242424242424242424888888242424242244884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111-1-1-1-1-1-1111-1-1-1-1-1111ii−i−i11-1-111-1-1-1i−i11-1-11iiii−i−i−i−i1111-1-1-1-1ii−i−ii−iii−i−i1-11-1i−i1-1i−i
χ1011111-1-1-1-1-1-1111-1-1-1-1-1111ii−i−i11-1-111-1-1-1i−i11-1-11iiii−i−i−i−i1111-1-1-1-1−i−iiii−iii−i−i-11-11−ii-11−ii
χ1111111-1-1-1-1-1-1111-1-1-1-1-1111ii−i−i11-1-111-1-1-1i−i-1-1111iiii−i−i−i−i-1-1-1-11111ii−i−i−ii−i−iii1-11-1i−i-11−ii
χ1211111-1-1-1-1-1-1111-1-1-1-1-1111ii−i−i11-1-111-1-1-1i−i-1-1111iiii−i−i−i−i-1-1-1-11111−i−iii−ii−i−iii-11-11−ii1-1i−i
χ1311111-1-1-1-1-1-1111-1-1-1-1-1111−i−iii11-1-111-1-1-1−ii11-1-11−i−i−i−iiiii1111-1-1-1-1ii−i−i−ii−i−iii-11-11i−i-11i−i
χ1411111-1-1-1-1-1-1111-1-1-1-1-1111−i−iii11-1-111-1-1-1−ii11-1-11−i−i−i−iiiii1111-1-1-1-1−i−iii−ii−i−iii1-11-1−ii1-1−ii
χ1511111-1-1-1-1-1-1111-1-1-1-1-1111−i−iii11-1-111-1-1-1−ii-1-1111−i−i−i−iiiii-1-1-1-11111ii−i−ii−iii−i−i-11-11i−i1-1−ii
χ1611111-1-1-1-1-1-1111-1-1-1-1-1111−i−iii11-1-111-1-1-1−ii-1-1111−i−i−i−iiiii-1-1-1-11111−i−iiii−iii−i−i1-11-1−ii-11i−i
χ1722222222-2-222222222-2-2-220000-2-22222-2-2-2000000-20000000000000000000000000022-2-2000000
χ1822222222-2-222222222-2-2-220000-2-22222-2-2-2000000-200000000000000000000000000-2-222000000
χ19222222-2222-22222222-2-22-2000022-2-2-2-222-2000000-2000000000000000022220000000000-2-20000
χ20222222-2222-22222222-2-22-2000022-2-2-2-222-2000000-20000000000000000-2-2-2-20000000000220000
χ21222222-22-2-2-2222222222-2-22i2i−2i−2i-2-2-2-2-2-2-2-22−2i2i000022i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ22222222-22-2-2-2222222222-2-2−2i−2i2i2i-2-2-2-2-2-2-2-222i−2i00002−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ2322222-22-2222222-2-2-2-2-22-2-22222-2-222-2-222-2-2-20000222-2-2-2-2220000000000000000000000000000
χ2422222-22-2222222-2-2-2-2-22-2-2-2-2-2-2-2-222-2-222-22200002-2-22222-2-20000000000000000000000000000
χ2522222-22-2-2-22222-2-2-2-22-22-200002222-2-2-2-22000000-200000000000000002i2i−2i−2i0000000000−2i2i0000
χ2622222-22-2-2-22222-2-2-2-22-22-200002222-2-2-2-22000000-20000000000000000−2i−2i2i2i00000000002i−2i0000
χ2722222-2-2-222-2222-2-2-2-22-2-220000-2-2-2-222222000000-2000000000000000000000000002-2-22000000
χ2822222-2-2-222-2222-2-2-2-22-2-220000-2-2-2-222222000000-200000000000000000000000000-222-2000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1111111110000-2-211110000000000
χ312222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-22222-111111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ322222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-11111111111111111000022-1-1-1-10000000000
χ332222-12-22-2-2-2-1-1-1-1-1-1-122-2-22i2i−2i−2i11111111-1−2i2i0000-1−i−iii−i−iii33−3−333−3−3000000−i3i3−i3i30000000000
χ342222-12-22-2-2-2-1-1-1-1-1-1-122-2-22i2i−2i−2i11111111-1−2i2i0000-1−i−iii−i−iii−3−333−3−333000000i3−i3i3−i30000000000
χ352222-12-22-2-2-2-1-1-1-1-1-1-122-2-2−2i−2i2i2i11111111-12i−2i0000-1ii−i−iii−i−i33−3−333−3−3000000i3−i3i3−i30000000000
χ362222-12-22-2-2-2-1-1-1-1-1-1-122-2-2−2i−2i2i2i11111111-12i−2i0000-1ii−i−iii−i−i−3−333−3−333000000−i3i3−i3i30000000000
χ372222-1-22-2222-1-1-11111-22-2-2222211-1-111-1-11-2-20000-1-1-11111-1-133−3−3−3−333000000−333−30000000000
χ382222-1-22-2222-1-1-11111-22-2-2222211-1-111-1-11-2-20000-1-1-11111-1-1−3−33333−3−30000003−3−330000000000
χ392222-1-22-2222-1-1-11111-22-2-2-2-2-2-211-1-111-1-11220000-111-1-1-1-11133−3−3−3−3330000003−3−330000000000
χ402222-1-22-2222-1-1-11111-22-2-2-2-2-2-211-1-111-1-11220000-111-1-1-1-111−3−33333−3−3000000−333−30000000000
χ412222-1-2-2-2-2-2-2-1-1-11111-22222i2i−2i−2i-1-111-1-11112i−2i22-2-2-1−i−i−i−iiiii-1-1-1-1111100002i−2i−i−iii0000000000
χ422222-1-2-2-2-2-2-2-1-1-11111-22222i2i−2i−2i-1-111-1-11112i−2i-2-222-1−i−i−i−iiiii1111-1-1-1-10000−2i2iii−i−i0000000000
χ432222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i2i2i-1-111-1-1111−2i2i22-2-2-1iiii−i−i−i−i-1-1-1-111110000−2i2iii−i−i0000000000
χ442222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i2i2i-1-111-1-1111−2i2i-2-222-1iiii−i−i−i−i1111-1-1-1-100002i−2i−i−iii0000000000
χ454444-2444-4-44-2-2-2-2-2-2-2-4-4-44000022-2-2-2-22220000002000000000000000000000000000000000000
χ464444-24-4444-4-2-2-2-2-2-2-2-4-44-40000-2-22222-2-220000002000000000000000000000000000000000000
χ474444-2-44-4-4-44-2-2-222224-44-40000-2-2-2-22222-20000002000000000000000000000000000000000000
χ484444-2-4-4-444-4-2-2-222224-4-4400002222-2-2-2-2-20000002000000000000000000000000000000000000
χ4944-4-4440-40004-4-444-4-4000000000000000000000000000000000000000022−2222−220000000000000000
χ5044-4-4440-40004-4-444-4-40000000000000000000000000000000000000000−2222−22220000000000000000
χ5144-4-44-4040004-4-4-4-4440000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5244-4-44-4040004-4-4-4-44400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ534-44-440004-40-44-40000000000000000004-40002i−2i2i−2i0000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ544-44-440004-40-44-40000000000000000004-4000−2i2i−2i2i000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ554-44-44000-440-44-4000000000000000000-440002i−2i−2i2i0000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ564-44-44000-440-44-4000000000000000000-44000−2i2i2i−2i000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ574-44-4-20004-402-2223−2323−230000000023−230000-220002i−2i2i−2i000000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000
χ584-44-4-20004-402-2223−2323−230000000023−230000-22000−2i2i−2i2i000000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000
χ594-44-4-20004-402-22−2323−232300000000−23230000-220002i−2i2i−2i000000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000
χ604-44-4-20004-402-22−2323−232300000000−23230000-22000−2i2i−2i2i000000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000
χ614-44-4-2000-4402-2223−2323−2300000000−232300002-20002i−2i−2i2i000000000ζ4+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
χ624-44-4-2000-4402-2223−2323−2300000000−232300002-2000−2i2i2i−2i000000000−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
χ634-44-4-2000-4402-22−2323−23230000000023−2300002-20002i−2i−2i2i000000000−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
χ644-44-4-2000-4402-22−2323−23230000000023−2300002-2000−2i2i2i−2i000000000ζ4−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
χ654-4-44404000-4-4-4400000000−2i22i2−2i22i2004-4000000000000−2i22i20000−2i22i20000000000000000000000000000
χ664-4-44404000-4-4-44000000002i2−2i22i2−2i2004-40000000000002i2−2i200002i2−2i20000000000000000000000000000
χ674-4-4440-40004-4-440000000022−22−222200-4400000000000022−220000−22220000000000000000000000000000
χ684-4-4440-40004-4-4400000000−222222−2200-44000000000000−2222000022−220000000000000000000000000000
χ694-4-44-204000-422-223−23−23230000−2i22i2−2i22i200-2223−230000000000i2−i2i6−i6i6−i6i2−i20000000000000000000000000000
χ704-4-44-204000-422-223−23−232300002i2−2i22i2−2i200-2223−230000000000−i2i2−i6i6−i6i6−i2i20000000000000000000000000000
χ714-4-44-204000-422-2−232323−230000−2i22i2−2i22i200-22−23230000000000i2−i2−i6i6−i6i6i2−i20000000000000000000000000000
χ724-4-44-204000-422-2−232323−2300002i2−2i22i2−2i200-22−23230000000000−i2i2i6−i6i6−i6−i2i20000000000000000000000000000
χ734-4-44-20-4000422-223−23−2323000022−22−2222002-2−23230000000000−226−6−662−20000000000000000000000000000
χ744-4-44-20-4000422-223−23−23230000−222222−22002-2−232300000000002−2−666−6−220000000000000000000000000000
χ754-4-44-20-4000422-2−232323−23000022−22−2222002-223−230000000000−22−666−62−20000000000000000000000000000
χ764-4-44-20-4000422-2−232323−230000−222222−22002-223−2300000000002−26−6−66−220000000000000000000000000000
χ7788-8-8-480-8000-444-4-444000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4-808000-44444-4-4000000000000000000000000000000000000000000000000000000000000

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