Finite Group Databasebeta

← Group #10776645

Character table — Group #10776645

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888161616161616161616162424242424242424242424244848
order122234444666244446612121212121212122244888812122424242424242424668812122424242422244444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1111111-1-1
χ911111-1-1-1-1111-1-1111-1-1-1-1-1-111111-11-111-1-1-111111-1-1-1-11-11-11-111-1-11-1111-1-1-111-1-11-1
χ1011111-1-1-1-1111-1-1111-1-1-1-1-1-111111-11-111-1-1-111111-1-1-1-11-11-11-111-1-1-11-1-1-1111-1-111-11
χ1111111-1-1-1-1111-1-1111-1-1-1-1-1-111111-11-1-1-111-11-1-1-1-111111-1-111-1-1-1111-1111-1-1-1-1-111-11
χ1211111-1-1-1-1111-1-1111-1-1-1-1-1-111111-11-1-1-111-11-1-1-1-111111-1-111-1-1-111-11-1-1-111111-1-11-1
χ1311111-1-1-1-1111-1-1111-1-1-1-1-1-11111-11-1111-1-1-111111-1-1-1-1-11-11-11-1-1111-1-1-11-11111-1-1-11
χ1411111-1-1-1-1111-1-1111-1-1-1-1-1-11111-11-1111-1-1-111111-1-1-1-1-11-11-11-1-111-1111-11-1-1-1-1111-1
χ1511111-1-1-1-1111-1-1111-1-1-1-1-1-11111-11-11-1-111-11-1-1-1-11111-111-1-1111-1-11-1-1-11-111-1-1111-1
χ1611111-1-1-1-1111-1-1111-1-1-1-1-1-11111-11-11-1-111-11-1-1-1-11111-111-1-1111-1-1-1111-11-1-111-1-1-11
χ17222222222222-2-22-2-2-2-2222222-2-200000000-2-2000000000000000000002-200-22000000
χ18222222222222-2-22-2-2-2-2222222-2-200000000-2-200000000000000000000-22002-2000000
χ192222222-2-22222-2-22-22222-2-2-2-22200000000-2-20000000000000000002-200-2200000000
χ202222222-2-22222-2-22-22222-2-2-2-22200000000-2-2000000000000000000-22002-200000000
χ212222222-2-2222-22-2-22-2-222-2-2-2-2-2-22-2-22000022000000002-200-22000000000000000000
χ222222222-2-2222-22-2-22-2-222-2-2-2-2-2-2-222-200002200000000-22002-2000000000000000000
χ2322222-2-2222222-2-2-2222-2-222-2-2-2-222-2-20000-22000000002200-2-2000000000000000000
χ2422222-2-2222222-2-2-2222-2-222-2-2-2-2-2-2220000-2200000000-2-20022000000000000000000
χ2522222-2-222222-22-22-2-2-2-2-222-2-222000000002-20000000000000000002200-2-200000000
χ2622222-2-222222-22-22-2-2-2-2-222-2-222000000002-2000000000000000000-2-2002200000000
χ2722222-2-2-2-2222222-2-222-2-2-2-222-2-2000000002-2000000000000000000002-2002-2000000
χ2822222-2-2-2-2222222-2-222-2-2-2-222-2-2000000002-200000000000000000000-2200-22000000
χ292222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000
χ302222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-2-2-1-1111100000000000000
χ312222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111-2-211111100000000000000
χ322222-12222-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111112211-1-1-1-100000000000000
χ332222-122-2-2-1-1-1-22-2-2211-1-11111112-2-220000-1-133−3−333−3−3-11001-13−33−300000000000000
χ342222-122-2-2-1-1-1-22-2-2211-1-11111112-2-220000-1-1−3−333−3−333-11001-1−33−3300000000000000
χ352222-122-2-2-1-1-1-22-2-2211-1-1111111-222-20000-1-133−3−333−3−31-100-11−33−3300000000000000
χ362222-122-2-2-1-1-1-22-2-2211-1-1111111-222-20000-1-1−3−333−3−3331-100-113−33−300000000000000
χ372222-1-2-222-1-1-12-2-2-22-1-111-1-1111122-2-200001-133−3−3−3−333-1-100113−3−3300000000000000
χ382222-1-2-222-1-1-12-2-2-22-1-111-1-1111122-2-200001-1−3−33333−3−3-1-10011−333−300000000000000
χ392222-1-2-222-1-1-12-2-2-22-1-111-1-11111-2-22200001-133−3−3−3−3331100-1-1−333−300000000000000
χ402222-1-2-222-1-1-12-2-2-22-1-111-1-11111-2-22200001-1−3−33333−3−31100-1-13−3−3300000000000000
χ412222-1-2-2-2-2-1-1-1-2-2222111111-1-1-1-12-22-222-2-21-1-1-1-1-11111-112-2-11-1-11100000000000000
χ422222-1-2-2-2-2-1-1-1-2-2222111111-1-1-1-12-22-2-2-2221-11111-1-1-1-1-11-22-1111-1-100000000000000
χ432222-1-2-2-2-2-1-1-1-2-2222111111-1-1-1-1-22-2222-2-21-1-1-1-1-111111-1-221-111-1-100000000000000
χ442222-1-2-2-2-2-1-1-1-2-2222111111-1-1-1-1-22-22-2-2221-11111-1-1-1-11-12-21-1-1-11100000000000000
χ454444-24444-2-2-2-4-44-4-422-2-2-2-2-2-222000000002200000000000000000000000000000000
χ464444-244-4-4-2-2-24-4-44-4-2-2-2-22222-2-2000000002200000000000000000000000000000000
χ474444-2-4-444-2-2-2-44-44-42222-2-222-2-200000000-2200000000000000000000000000000000
χ484444-2-4-4-4-4-2-2-2444-4-4-2-22222-2-22200000000-2200000000000000000000000000000000
χ4944-4-444i−4i004-4-400000004i−4i00000000002-22i−2i002-22-22i−2i2i−2i000000000000000000000000
χ5044-4-444i−4i004-4-400000004i−4i0000000000-22−2i2i00-22-22−2i2i−2i2i000000000000000000000000
χ5144-4-44−4i4i004-4-40000000−4i4i00000000002-2−2i2i002-22-2−2i2i−2i2i000000000000000000000000
χ5244-4-44−4i4i004-4-40000000−4i4i0000000000-222i−2i00-22-222i−2i2i−2i000000000000000000000000
χ5344-4-4-24i−4i00-22200000−2i32i3−2i2i000023−2300002-22i−2i00−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ5444-4-4-24i−4i00-22200000−2i32i3−2i2i000023−230000-22−2i2i001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ5544-4-4-24i−4i00-222000002i3−2i3−2i2i0000−232300002-22i−2i00−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ5644-4-4-24i−4i00-222000002i3−2i3−2i2i0000−23230000-22−2i2i001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ5744-4-4-2−4i4i00-22200000−2i32i32i−2i0000−232300002-2−2i2i00−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ5844-4-4-2−4i4i00-22200000−2i32i32i−2i0000−23230000-222i−2i001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ5944-4-4-2−4i4i00-222000002i3−2i32i−2i000023−2300002-2−2i2i00−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ6044-4-4-2−4i4i00-222000002i3−2i32i−2i000023−230000-222i−2i001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ614-4-444004-4-4-440000000004-400000000000000000000000000000000000000002-22-200
χ624-4-444004-4-4-440000000004-40000000000000000000000000000000000000000-22-2200
χ634-4-44400-44-4-44000000000-4400000000000000000000000000000000000000002-2-2200
χ644-4-44400-44-4-44000000000-440000000000000000000000000000000000000000-222-200
χ658-88-880000-88-8000000000000000000000000000000000000000000000000000000000
χ668-88-8-400004-440000000000043−4300000000000000000000000000000000000000000000
χ678-88-8-400004-4400000000000−434300000000000000000000000000000000000000000000
χ688-8-88-4008-844-4000000000-440000000000000000000000000000000000000000000000
χ698-8-88-400-8844-40000000004-40000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.