Finite Group Databasebeta

← Group #10770256

Character table — Group #10770256

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888161616161616161616162424242424242424242424244848
order122222223666244446666661212121224444444121212121212121212126881212122424242422444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1111111-1-1
χ911111-1-111111-1-1-1111-1-1-1-11-1-1111-1-1111-1-11-11111-1-1-1-111-11-1-111-1-11-11-11-11-111-1-11-1
χ1011111-1-111111-1-1-1111-1-1-1-11-1-1111-1-1111-1-11-11111-1-1-1-111-11-1-111-1-1-11-11-11-11-1-111-11
χ1111111-1-111111-1-1-1111-1-1-1-11-1-1111-1-11-1-1111-1-1-1-1-111111-111-1-1-1-1111-11-11-11-1-1-111-11
χ1211111-1-111111-1-1-1111-1-1-1-11-1-1111-1-11-1-1111-1-1-1-1-111111-111-1-1-1-111-11-11-11-1111-1-11-1
χ1311111-1-111111-1-1-1111-1-1-1-11-1-111-111-111-1-11-11111-1-1-1-1-1-11-111-1-1111-1-111-1-1111-1-1-11
χ1411111-1-111111-1-1-1111-1-1-1-11-1-111-111-111-1-11-11111-1-1-1-1-1-11-111-1-111-111-1-111-1-1-1111-1
χ1511111-1-111111-1-1-1111-1-1-1-11-1-111-111-1-1-1111-1-1-1-1-11111-11-1-11111-1-11-1-111-1-11-1-1111-1
χ1611111-1-111111-1-1-1111-1-1-1-11-1-111-111-1-1-1111-1-1-1-1-11111-11-1-11111-1-1-111-1-111-111-1-1-11
χ172222222222222-2-2-2-2222222-2-2-2-200000000-2-2000000000000000000002-200-22000000
χ182222222222222-2-2-2-2222222-2-2-2-200000000-2-200000000000000000000-22002-2000000
χ1922222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-100000000000000
χ2022222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-2-2-1-1-1111100000000000000
χ2122222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-11-2-2111111100000000000000
χ2222222222-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111122111-1-1-1-100000000000000
χ2322222-2-222222-222-2-22-2-2-2-2222-2-200000000-22000000000000000000002200-2-2000000
χ2422222-2-222222-222-2-22-2-2-2-2222-2-200000000-2200000000000000000000-2-20022000000
χ2522222-2-22-1-1-1-1-2-2-222-11111-111-1-12-2-2222-2-2-11-1-1-1-11111-12-2-111-1-11100000000000000
χ2622222-2-22-1-1-1-1-2-2-222-11111-111-1-12-2-22-2-222-111111-1-1-1-1-1-22-11111-1-100000000000000
χ2722222-2-22-1-1-1-1-2-2-222-11111-111-1-1-222-222-2-2-11-1-1-1-111111-221-1-111-1-100000000000000
χ2822222-2-22-1-1-1-1-2-2-222-11111-111-1-1-222-2-2-222-111111-1-1-1-112-21-1-1-1-11100000000000000
χ292222-222-22222-22-22-2-222-2-2-2222200000000-2-20000000000000000002200-2-200000000
χ302222-222-22222-22-22-2-222-2-2-2222200000000-2-2000000000000000000-2-2002200000000
χ312222-222-22222-2-22-22-222-2-2-2-2-2-2-222-2-200002200000000200-22-2000000000000000000
χ322222-222-22222-2-22-22-222-2-2-2-2-2-2-2-2-22200002200000000-2002-22000000000000000000
χ332222-222-2-1-1-1-1-2-22-221-1-1111111122-2-20000-1-133−3−333−3−3-1001-113−33−300000000000000
χ342222-222-2-1-1-1-1-2-22-221-1-1111111122-2-20000-1-1−3−333−3−333-1001-11−33−3300000000000000
χ352222-222-2-1-1-1-1-2-22-221-1-11111111-2-2220000-1-133−3−333−3−3100-11-1−33−3300000000000000
χ362222-222-2-1-1-1-1-2-22-221-1-11111111-2-2220000-1-1−3−333−3−333100-11-13−33−300000000000000
χ372222-2-2-2-2222222-2-22-2-2-222-222-2-22-22-200002-200000000200-2-22000000000000000000
χ382222-2-2-2-2222222-2-22-2-2-222-222-2-2-22-2200002-200000000-20022-2000000000000000000
χ392222-2-2-2-222222-222-2-2-2-222-2-2-22200000000-220000000000000000002-200-2200000000
χ402222-2-2-2-222222-222-2-2-2-222-2-2-22200000000-22000000000000000000-22002-200000000
χ412222-2-2-2-2-1-1-1-122-2-22111-1-11-1-1112-22-20000-1133−3−3−3−333-10011-13−3−3300000000000000
χ422222-2-2-2-2-1-1-1-122-2-22111-1-11-1-1112-22-20000-11−3−33333−3−3-10011-1−333−300000000000000
χ432222-2-2-2-2-1-1-1-122-2-22111-1-11-1-111-22-220000-1133−3−3−3−333100-1-11−333−300000000000000
χ442222-2-2-2-2-1-1-1-122-2-22111-1-11-1-111-22-220000-11−3−33333−3−3100-1-113−3−3300000000000000
χ4544444444-2-2-2-24-4-4-4-4-2-2-2-2-2-22222000000002200000000000000000000000000000000
χ4644444-4-44-2-2-2-2-444-4-4-22222-2-2-222000000002-200000000000000000000000000000000
χ474444-444-4-2-2-2-2-44-44-42-2-2222-2-2-2-2000000002200000000000000000000000000000000
χ484444-4-4-4-4-2-2-2-24-444-4222-2-2222-2-2000000002-200000000000000000000000000000000
χ4944-4-404-4044-4-40000004-4000000000002-22-2002-22-22-22-2000000000000000000000000
χ5044-4-404-4044-4-40000004-400000000000-22-2200-22-22-22-22000000000000000000000000
χ5144-4-404-40-2-222000000-2200023−2323−2300002-22-200−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000
χ5244-4-404-40-2-222000000-2200023−2323−230000-22-22001−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000
χ5344-4-404-40-2-222000000-22000−2323−232300002-22-200−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000
χ5444-4-404-40-2-222000000-22000−2323−23230000-22-22001+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000
χ5544-4-40-44044-4-4000000-44000000000002-2-22002-22-2-22-22000000000000000000000000
χ5644-4-40-44044-4-4000000-4400000000000-222-200-22-222-22-2000000000000000000000000
χ5744-4-40-440-2-2220000002-200023−23−232300002-2-2200−1−31+3−1+31−31+3−1−31−3−1+3000000000000000000000000
χ5844-4-40-440-2-2220000002-200023−23−23230000-222-2001+3−1−31−3−1+3−1−31+3−1+31−3000000000000000000000000
χ5944-4-40-440-2-2220000002-2000−232323−2300002-2-2200−1+31−3−1−31+31−3−1+31+3−1−3000000000000000000000000
χ6044-4-40-440-2-2220000002-2000−232323−230000-222-2001−3−1+31+3−1−3−1+31−3−1−31+3000000000000000000000000
χ614-4-44400-44-44-40000040000-40000000000000000000000000000000000000000−2i22i20000
χ624-4-44400-44-44-40000040000-400000000000000000000000000000000000000002i2−2i20000
χ634-4-44-40044-44-400000-40000400000000000000000000000000000000000000000022−2200
χ644-4-44-40044-44-400000-400004000000000000000000000000000000000000000000−222200
χ658-88-800008-8-88000000000000000000000000000000000000000000000000000000000
χ668-88-80000-444-400000000−4i34i300000000000000000000000000000000000000000000000
χ678-88-80000-444-4000000004i3−4i300000000000000000000000000000000000000000000000
χ688-8-88800-8-44-4400000-4000040000000000000000000000000000000000000000000000
χ698-8-88-8008-44-440000040000-40000000000000000000000000000000000000000000000

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