Finite Group Databasebeta

← Group #10778210

Character table — Group #10778210

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12223444444446661212121224444441212121212121212246668888121212121212122424242424242424888824661212888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-111-1-111111111-1-11-1-11111-1-1-1-11-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111-1-111-1-111111111-1-11-1-11111-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-111-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-111-1-111111111-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ911111-1-1-1-11111111-1-1-1-1-111-111111-1-1-1-111-1-1-1-1-111-1-111-1-11111111-1-1-1-111-1-11-111-1-11-111-1-111-1-11-1
χ1011111-1-1-1-11111111-1-1-1-1-111-111111-1-1-1-111-1-1-1-1-111-1-111-1-11111111-1-1-1-1-1-1111-111-1-1-11-1-111-1-111-11
χ1111111-1-1-1-11111111-1-1-1-1-111-111111-1-1-1-111-1-1-1-1-1-1-11111-1-1111-1-1-1-1111111-1-1-11-1-1111-111-1-1-1-111-11
χ1211111-1-1-1-11111111-1-1-1-1-111-111111-1-1-1-111-1-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-111-11-1-111-11-1-11111-1-11-1
χ1311111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-11111-1-1-1-1111-1-11111-1-1-1-111-1-1-11-1-1111-1-1-11111-1-1-11
χ1411111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-11111-1-1-1-1111-1-11111-1-1-1-1-1-111-11-1-111-1111-1-1-1-1111-1
χ1511111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-111-1-111-1-1111-1-1-1-1-1-1111111-1-11-111-1-11-1-1-111-1-1111-1
χ1611111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-111-1-111-1-1111-1-1-1-1-1-11111-1-1111-111-1-1-1111-1-111-1-1-11
χ17222222222-222-22222222-200-2-2002222-2-2-2-200-20000000000-200000000002222000000-2-20000000000
χ18222222222-222-22222222-200-2-2002222-2-2-2-200-20000000000-20000000000-2-2-2-2000000220000000000
χ192222222-2-22-2-22222-2-2-2-2222-2-2-2-2-2-222-2-2222-2222000022-2-2-2-2-2000000000000000000000000000000
χ202222222-2-22-2-22222-2-2-2-22-2-2-2-222-2-222-2-222-222-2-20000-2-222-222000000000000000000000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-2-2002200-2-22222-2-200-20000000000200000000000000000000002i−2i2i−2i000000
χ222222222-2-2-2-2-2-2222-2-2-2-2-2002200-2-22222-2-200-2000000000020000000000000000000000−2i2i−2i2i000000
χ2322222-2-2222-2-222222222-2222-2-2-2-2-2-2-22222-22-2-2-200002222-2-2-2000000000000000000000000000000
χ2422222-2-2222-2-222222222-2-2-22-222-2-2-2-222222-2-2220000-2-2-2-2-222000000000000000000000000000000
χ2522222-2-222-2-2-2-22222222200-2200-2-2-2-2-2-2-2-20020000000000200000000000000000000002i−2i−2i2i000000
χ2622222-2-222-2-2-2-22222222200-2200-2-2-2-2-2-2-2-2002000000000020000000000000000000000−2i2i2i−2i000000
χ2722222-2-2-2-2-222-2222-2-2-2-22002-20022-2-222-2-20020000000000-2000000000022-2-2000000-220000000000
χ2822222-2-2-2-2-222-2222-2-2-2-22002-20022-2-222-2-20020000000000-20000000000-2-2220000002-20000000000
χ292222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ302222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1111111110000-2-21111000000000000
χ312222-122222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2-11122221111-111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ322222-122222222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-2-2-111-2-2-2-21111-11111111111000022-1-1-1-1000000000000
χ332222-122-2-22-2-22-1-1-11111222-2-2-2-211-1-111-1-12-2-1-1-10000-1-111111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ342222-122-2-22-2-22-1-1-11111222-2-2-2-211-1-111-1-12-2-1-1-10000-1-111111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ352222-122-2-22-2-22-1-1-111112-2-2-2-22211-1-111-1-1-22-111000011-1-11-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ362222-122-2-22-2-22-1-1-111112-2-2-2-22211-1-111-1-1-22-111000011-1-11-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ372222-1-2-2222-2-22-1-1-1-1-1-1-1-2222-2-2-21111-1-1-1-1-221110000-1-1-1-1111−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ382222-1-2-2222-2-22-1-1-1-1-1-1-1-2222-2-2-21111-1-1-1-1-221110000-1-1-1-1111i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ392222-1-2-2222-2-22-1-1-1-1-1-1-1-2-2-22-2221111-1-1-1-12-21-1-1000011111-1-1−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ402222-1-2-2222-2-22-1-1-1-1-1-1-1-2-2-22-2221111-1-1-1-12-21-1-1000011111-1-1i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ412222-1-2-2-2-22222-1-1-11111-222-2222-1-11111-1-1-2-211122-2-2-1-111-1-1-1-1-1-1-1111100002-2-1-111000000000000
χ422222-1-2-2-2-22222-1-1-11111-222-2222-1-11111-1-1-2-2111-2-222-1-111-1-1-11111-1-1-1-10000-2211-1-1000000000000
χ432222-1-2-2-2-22222-1-1-11111-2-2-2-22-2-2-1-11111-1-1221-1-122-2-211-1-1-111-1-1-1-111110000-2211-1-1000000000000
χ442222-1-2-2-2-22222-1-1-11111-2-2-2-22-2-2-1-11111-1-1221-1-1-2-22211-1-1-1111111-1-1-1-100002-2-1-111000000000000
χ452-22-222i−2i2i−2i02-202-2-22i2i−2i−2i00000002-22i−2i000000000−i2i22−20000000−i2i2−i2i22−22−22-22i−2i000000000000−i2i22−200
χ462-22-222i−2i2i−2i02-202-2-22i2i−2i−2i00000002-22i−2i000000000−i2i22−20000000−i2i2−i2i22−22−2-22−2i2i000000000000i2−i2−2200
χ472-22-222i−2i2i−2i02-202-2-22i2i−2i−2i00000002-22i−2i000000000i2−i2−220000000i2−i2i2−i2−22−222-22i−2i000000000000i2−i2−2200
χ482-22-222i−2i2i−2i02-202-2-22i2i−2i−2i00000002-22i−2i000000000i2−i2−220000000i2−i2i2−i2−22−22-22−2i2i000000000000−i2i22−200
χ492-22-22−2i2i−2i2i02-202-2-2−2i−2i2i2i00000002-2−2i2i000000000−i2i2−220000000−i2i2−i2i2−22−222-2−2i2i000000000000−i2i2−2200
χ502-22-22−2i2i−2i2i02-202-2-2−2i−2i2i2i00000002-2−2i2i000000000−i2i2−220000000−i2i2−i2i2−22−22-222i−2i000000000000i2−i22−200
χ512-22-22−2i2i−2i2i02-202-2-2−2i−2i2i2i00000002-2−2i2i000000000i2−i22−20000000i2−i2i2−i22−22−22-2−2i2i000000000000i2−i22−200
χ522-22-22−2i2i−2i2i02-202-2-2−2i−2i2i2i00000002-2−2i2i000000000i2−i22−20000000i2−i2i2−i22−22−2-222i−2i000000000000−i2i2−2200
χ534444-24444-444-4-2-2-2-2-2-2-2-400-4-400-2-2-2-222220020000000000200000000000000000000000000000000
χ544444-244-4-4-4-4-4-4-2-2-22222-400440022-2-2-2-2220020000000000-200000000000000000000000000000000
χ554444-2-4-444-4-4-4-4-2-2-2-2-2-2-2400-44002222222200-20000000000-200000000000000000000000000000000
χ564444-2-4-4-4-4-444-4-2-2-222224004-400-2-222-2-22200-20000000000200000000000000000000000000000000
χ5744-4-440000400-4-44-4000004-400000000004-40000000004-400000000000000000000000000000000000
χ5844-4-440000400-4-44-400000-4400000000004-4000000000-4400000000000000000000000000000000000
χ5944-4-440000-4004-44-40000000004i−4i000000-44000000000000004i−4i000000000000000000000000000000
χ6044-4-440000-4004-44-4000000000−4i4i000000-4400000000000000−4i4i000000000000000000000000000000
χ6144-4-4-20000400-42-2223−2323−2304-40000000023−23-22000000000-2223−23000000000000000000000000000000000
χ6244-4-4-20000400-42-2223−2323−230-440000000023−23-220000000002-2−2323000000000000000000000000000000000
χ6344-4-4-20000400-42-22−2323−232304-400000000−2323-22000000000-22−2323000000000000000000000000000000000
χ6444-4-4-20000400-42-22−2323−23230-4400000000−2323-220000000002-223−23000000000000000000000000000000000
χ6544-4-4-20000-40042-2223−2323−23000004i−4i0000−23232-2000−2i32i3000000000−2i2i000000000000000000000000000000
χ6644-4-4-20000-40042-2223−2323−2300000−4i4i0000−23232-20002i3−2i30000000002i−2i000000000000000000000000000000
χ6744-4-4-20000-40042-22−2323−2323000004i−4i000023−232-20002i3−2i3000000000−2i2i000000000000000000000000000000
χ6844-4-4-20000-40042-22−2323−232300000−4i4i000023−232-2000−2i32i30000000002i−2i000000000000000000000000000000
χ694-44-444i−4i−4i4i0-4404-4-4−4i−4i4i4i0000000-444i−4i00000000000000000000000000000000000000000000000000
χ704-44-44−4i4i4i−4i0-4404-4-44i4i−4i−4i0000000-44−4i4i00000000000000000000000000000000000000000000000000
χ714-44-4-24i−4i4i−4i04-40-222−2i−2i2i2i0000000-22−2i2i000000000−2i22i222−220000000i2−i2i2−i2−22−220000000000000000000000
χ724-44-4-24i−4i4i−4i04-40-222−2i−2i2i2i0000000-22−2i2i0000000002i2−2i2−22220000000−i2i2−i2i22−22−20000000000000000000000
χ734-44-4-24i−4i−4i4i0-440-2222i2i−2i−2i00000002-2−2i2i000000000000000000006−6−66i6−i6−i6i60000000000000000000000
χ744-44-4-24i−4i−4i4i0-440-2222i2i−2i−2i00000002-2−2i2i00000000000000000000−666−6−i6i6i6−i60000000000000000000000
χ754-44-4-2−4i4i4i−4i0-440-222−2i−2i2i2i00000002-22i−2i000000000000000000006−6−66−i6i6i6−i60000000000000000000000
χ764-44-4-2−4i4i4i−4i0-440-222−2i−2i2i2i00000002-22i−2i00000000000000000000−666−6i6−i6−i6i60000000000000000000000
χ774-44-4-2−4i4i−4i4i04-40-2222i2i−2i−2i0000000-222i−2i000000000−2i22i2−22220000000i2−i2i2−i22−22−20000000000000000000000
χ784-44-4-2−4i4i−4i4i04-40-2222i2i−2i−2i0000000-222i−2i0000000002i2−2i222−220000000−i2i2−i2i2−22−220000000000000000000000
χ798-8-88800000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-40000000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000
χ818-8-88-40000000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000

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