Finite Group Databasebeta

← Group #10840271

Character table — Group #10840271

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order12442223444688881212666881212122424242444442224446688121224242424242444888866881212242424244444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-111-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-11-1-11111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1
χ9111111111111-1-1-1-111111-1-1111-1-1-1-111111-111-1111-1-111-1-1-1-1-1-111-1-1-1-11-11-11-111-1-1-1-111-1-1111-1
χ10111111111111-1-1-1-111111-1-1111-1-1-1-111111-1-11-1-1-1-111-1-1-1-1111111-1-1-1-11-1-111-1-1-1111111-1-1-1-1-11
χ11111111111111-1-1-1-111111-1-1111-1-1-1-11111-111-11111-1-111-1-1-1-1-1-111-1-1-1-1-11-11-11-1-111-1-1-1-11111-11
χ12111111111111-1-1-1-111111-1-1111-1-1-1-11111-11-1-11-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1111-1-111-1-111-1-11-1
χ13111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-11-111-1111-1-111-1-1-1-1-1-1-1-111111-11-11-111-1-111-1-111-1-1-11
χ14111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-11111-1-111111-1-111-1-1-111-1-1-1-111111-1
χ15111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1-1-1-11111-11-11-11-1-1111111-1-1-1-11-1
χ16111111111111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-1-1-11111-1-11111-111-1-1111-1-1-1-111-1-111-11
χ172222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000222222-1-122-1-1-1-1-1-1-1-1000000-1-122-1-1-1-1-1-10000000000
χ182222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1000022-222-211-2-211-1-11111000000-1-1-2-2-1-111110000000000
χ192222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-22-2-22-1-122-1-1-1-1-1-1-1-100000011-2-21111110000000000
χ202222222-1222-12222-1-1-1-1-122-1-1-1-1-1-1-10000-2-2-2-2-2-211-2-211-1-11111000000112211-1-1-1-10000000000
χ212222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-1111100002-222-22-1-1-2-2-1-1111111000000-112-2-11-1-1110000000000
χ222222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-1111100002-2-22-2-211221111-1-1-1-1000000-11-22-1111-1-10000000000
χ232222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-111110000-222-222-1-1-2-2-1-11111110000001-1-221-111-1-10000000000
χ242222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-1-1-111110000-22-2-22-211221111-1-1-1-10000001-12-21-1-1-1110000000000
χ2522222-2-22-22-222222222-2-2-2-2-22-222220000000000000000-2-200000000000000000000002i−2i2i−2i0000
χ2622222-2-22-22-222222222-2-2-2-2-22-222220000000000000000-2-20000000000000000000000−2i2i−2i2i0000
χ2722222-2-22-22-22-2-2-2-2222-2-222-22-2-2-2-2-200000000000000002200000000000000000000002i−2i−2i2i0000
χ2822222-2-22-22-22-2-2-2-2222-2-222-22-2-2-2-2-20000000000000000220000000000000000000000−2i2i2i−2i0000
χ292222-2-2222-2-22000022-22-2002-2-200002222000000002i−2i00002i2i−2i−2i-2-2000000000000002i−2i00000000
χ302222-2-2222-2-22000022-22-2002-2-20000222200000000−2i2i0000−2i−2i2i2i-2-200000000000000−2i2i00000000
χ312222-2-2222-2-22000022-22-2002-2-20000-2-2-2-2000000002i−2i00002i2i−2i−2i2200000000000000−2i2i00000000
χ322222-2-2222-2-22000022-22-2002-2-20000-2-2-2-200000000−2i2i0000−2i−2i2i2i22000000000000002i−2i00000000
χ3322-2-22-2-222-2220000-2-22-2-2002-2200002i2i−2i−2i00200-22200-2-20000002i−2i000000000000000000002i−2i00
χ3422-2-22-2-222-2220000-2-22-2-2002-2200002i2i−2i−2i00-2002-2-200220000002i−2i00000000000000000000−2i2i00
χ3522-2-22-2-222-2220000-2-22-2-2002-220000−2i−2i2i2i00200-22200-2-2000000−2i2i00000000000000000000−2i2i00
χ3622-2-22-2-222-2220000-2-22-2-2002-220000−2i−2i2i2i00-2002-2-20022000000−2i2i000000000000000000002i−2i00
χ3722-2-2-22-2222-2222-2-2-2-2-2-222-222-222-2-22i2i−2i−2i0000000000002-20000−2i2i2i2i−2i−2i00000000000000000000
χ3822-2-2-22-2222-2222-2-2-2-2-2-222-222-222-2-2−2i−2i2i2i0000000000002-200002i−2i−2i−2i2i2i00000000000000000000
χ3922-2-2-22-2222-22-2-222-2-2-2-22-2222-2-2-2222i2i−2i−2i000000000000-220000−2i2i−2i−2i2i2i00000000000000000000
χ4022-2-2-22-2222-22-2-222-2-2-2-22-2222-2-2-222−2i−2i2i2i000000000000-2200002i−2i2i2i−2i−2i00000000000000000000
χ4122-2-2-2-222-222222-2-2-2-2-22-2-22-22222-2-20000220-2-20000000-2200000000002200-2-200000000000000
χ4222-2-2-2-222-222222-2-2-2-2-22-2-22-22222-2-20000-2-20220000000-220000000000-2-2002200000000000000
χ4322-2-2-2-222-2222-2-222-2-2-22-22-2-222-2-22200002-20-2200000002-200000000002-200-2200000000000000
χ4422-2-2-2-222-2222-2-222-2-2-22-22-2-222-2-2220000-2202-200000002-20000000000-22002-200000000000000
χ4522-2-2-2-22-1-222-122-2-2111-11-221-1-1-1-1110000220-2-20−i3i300−i3i31-1−i3i3−i3i3000000-1-10011−i3i3−i3i30000000000
χ4622-2-2-2-22-1-222-122-2-2111-11-221-1-1-1-1110000220-2-20i3−i300i3−i31-1i3−i3i3−i3000000-1-10011i3−i3i3−i30000000000
χ4722-2-2-2-22-1-222-122-2-2111-11-221-1-1-1-1110000-2-20220−i3i300−i3i31-1−i3i3−i3i30000001100-1-1i3−i3i3−i30000000000
χ4822-2-2-2-22-1-222-122-2-2111-11-221-1-1-1-1110000-2-20220i3−i300i3−i31-1i3−i3i3−i30000001100-1-1−i3i3−i3i30000000000
χ4922-2-2-2-22-1-222-1-2-222111-112-21-1-111-1-100002-20-220−i3i300−i3i3-11i3−i3i3−i3000000-11001-1−i3i3i3−i30000000000
χ5022-2-2-2-22-1-222-1-2-222111-112-21-1-111-1-100002-20-220i3−i300i3−i3-11−i3i3−i3i3000000-11001-1i3−i3−i3i30000000000
χ5122-2-2-2-22-1-222-1-2-222111-112-21-1-111-1-10000-2202-20−i3i300−i3i3-11i3−i3i3−i30000001-100-11i3−i3−i3i30000000000
χ5222-2-2-2-22-1-222-1-2-222111-112-21-1-111-1-10000-2202-20i3−i300i3−i3-11−i3i3−i3i30000001-100-11−i3i3i3−i30000000000
χ5344444-4-4-2-44-4-24444-2-2-222-4-42-22-2-2-2-2000000000000000022000000000000000000000000000000
χ5444444-4-4-2-44-4-2-4-4-4-4-2-2-222442-2222220000000000000000-2-2000000000000000000000000000000
χ554444-44-44-4-444000044-4-4400-4-440000000000000000000000000000000000000000000000000000
χ564444-44-4-2-4-44-20000-2-222-20022-200000000000000−2i32i3002i3−2i300000000000000000000000000000000
χ574444-44-4-2-4-44-20000-2-222-20022-2000000000000002i3−2i300−2i32i300000000000000000000000000000000
χ584444-4-44-24-4-4-20000-2-22-2200-22200000000000000004i−4i0000−2i−2i2i2i00000000000000000000000000
χ594444-4-44-24-4-4-20000-2-22-2200-2220000000000000000−4i4i00002i2i−2i−2i00000000000000000000000000
χ6044-4-44444-4-4-440000-4-444400-4-4-40000000000000000000000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2000022-2-2-200222000000000000000000000023−23−232300000000000000000000000000
χ6244-4-4444-2-4-4-4-2000022-2-2-2002220000000000000000000000−232323−2300000000000000000000000000
χ6344-4-44-4-4-24-44-2000022-22200-22-20000000000400-4-2-2002200000000000000000000000000000000
χ6444-4-44-4-4-24-44-2000022-22200-22-20000000000-40042200-2-200000000000000000000000000000000
χ6544-4-4-44-4-244-4-244-4-42222-24-4-2-22-2-2220000000000000000-22000000000000000000000000000000
χ6644-4-4-44-4-244-4-2-4-4442222-2-44-2-2222-2-200000000000000002-2000000000000000000000000000000
χ674-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i22+2i−2−2i2−2i−2+2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ684-44i−4i0004000-422−22−2i22i24i−4i0000000022−22−2i22i2−2−2i2+2i−2+2i2−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ694-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i22+2i−2−2i2−2i−2+2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ704-44i−4i0004000-4−22222i2−2i24i−4i00000000−22222i2−2i2−2−2i2+2i−2+2i2−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ714-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i22−2i−2+2i2+2i−2−2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ724-4−4i4i0004000-422−222i2−2i2−4i4i0000000022−222i2−2i2−2+2i2−2i−2−2i2+2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ734-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i22−2i−2+2i2+2i−2−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ744-4−4i4i0004000-4−2222−2i22i2−4i4i00000000−2222−2i22i2−2+2i2−2i−2−2i2+2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ758-88i−8i000-4000442−42−4i24i2−4i4i00000000−22222i2−2i2000000000000000000000000000000000000000000000000
χ768-88i−8i000-40004−42424i2−4i2−4i4i0000000022−22−2i22i2000000000000000000000000000000000000000000000000
χ778-8−8i8i000-4000442−424i2−4i24i−4i00000000−2222−2i22i2000000000000000000000000000000000000000000000000
χ788-8−8i8i000-40004−4242−4i24i24i−4i0000000022−222i2−2i2000000000000000000000000000000000000000000000000

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