Finite Group Databasebeta

← Group #10696818

Character table — Group #10696818

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order12222234466644444661212121212121212888812122424242424242424448812121212242424248888222488
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111
χ9222222222222-2-2-22-222-2-22222-2-20000-2-2000000000000000000000000002-200
χ10222222222222-2-2-22-222-2-22222-2-20000-2-200000000000000000000000000-2200
χ112222222-2-222222-2-2-22222-2-2-2-2-2-200002-200000000002i−2i00002i2i−2i−2i0000000000
χ122222222-2-222222-2-2-22222-2-2-2-2-2-200002-20000000000−2i2i0000−2i−2i2i2i0000000000
χ132222222-2-2222-2-22-2222-2-2-2-2-2-2220000-220000000000000000000022-2-2000000
χ142222222-2-2222-2-22-2222-2-2-2-2-2-2220000-2200000000000000000000-2-222000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-10000000000
χ19222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-113333−3−3−3−3002i−2i−i3−i3i3i3−i−iii0000000000
χ20222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-113333−3−3−3−300−2i2ii3i3−i3−i3ii−i−i0000000000
χ21222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-11−3−3−3−33333002i−2ii3i3−i3−i3−i−iii0000000000
χ22222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-11−3−3−3−3333300−2i2i−i3−i3i3i3ii−i−i0000000000
χ232222-2-22222222-22-2-2-2-22222-2-2220000-2-200000000000000000000000000002-2
χ242222-2-22222222-22-2-2-2-22222-2-2220000-2-20000000000000000000000000000-22
χ252222-2-2222222-22-2-22-2-2-2-222-2-2-2-2000022000000002-2002-22-200000000000000
χ262222-2-2222222-22-2-22-2-2-2-222-2-2-2-200002200000000-2200-22-2200000000000000
χ272222-2-22-2-22222-2-222-2-222-2-222-2-20000-220000000000000000000000002-20000
χ282222-2-22-2-22222-2-222-2-222-2-222-2-20000-22000000000000000000000000-220000
χ292222-2-22-2-2222-2222-2-2-2-2-2-2-2222222-2-22-222-2-222-2-20000000000000000000000
χ302222-2-22-2-2222-2222-2-2-2-2-2-2-22222-2-2222-2-2-222-2-2220000000000000000000000
χ312222-2-2-122-1-1-1-22-2-221111-1-111110000-1-133−3−3−3−3332-200-11-113−33−30000000000
χ322222-2-2-122-1-1-1-22-2-221111-1-111110000-1-133−3−3−3−333-22001-11-1−33−330000000000
χ332222-2-2-122-1-1-1-22-2-221111-1-111110000-1-1−3−33333−3−32-200-11-11−33−330000000000
χ342222-2-2-122-1-1-1-22-2-221111-1-111110000-1-1−3−33333−3−3-22001-11-13−33−30000000000
χ352222-2-2-1-2-2-1-1-1-2222-2111111-1-1-1-122-2-2-11-1-111-1-1110000−i3i3i3−i3−i3i3i3−i30000000000
χ362222-2-2-1-2-2-1-1-1-2222-2111111-1-1-1-122-2-2-11-1-111-1-1110000i3−i3−i3i3i3−i3−i3i30000000000
χ372222-2-2-1-2-2-1-1-1-2222-2111111-1-1-1-1-2-222-1111-1-111-1-10000−i3i3i3−i3i3−i3−i3i30000000000
χ382222-2-2-1-2-2-1-1-1-2222-2111111-1-1-1-1-2-222-1111-1-111-1-10000i3−i3−i3i3−i3i3i3−i30000000000
χ39444444-244-2-2-2-4-4-44-4-2-222-2-2-2-222000022000000000000000000000000000000
χ40444444-2-4-4-2-2-2-4-44-44-2-2222222-2-200002-2000000000000000000000000000000
χ414444-4-4-244-2-2-24-44-4-422-2-2-2-222-2-2000022000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-24-4-44422-2-222-2-22200002-2000000000000000000000000000000
χ4344-4-44-44004-4-4000004-4000000000000000000000000000000000000−2i22i2000000
χ4444-4-44-44004-4-4000004-40000000000000000000000000000000000002i2−2i2000000
χ4544-4-4-444004-4-400000-440000000000000000000000000000000000−2i22i200000000
χ4644-4-4-444004-4-400000-4400000000000000000000000000000000002i2−2i200000000
χ474-4-440044-4-44-40000000004-400002-22-2002-22-22-22-20000000000000000000000
χ484-4-440044-4-44-40000000004-40000-22-2200-22-22-22-220000000000000000000000
χ494-4-44004-44-44-4000000000-4400002-2-22002-2-222-2-220000000000000000000000
χ504-4-44004-44-44-4000000000-440000-222-200-222-2-222-20000000000000000000000
χ514-4-4400-24-42-22000000023−23-220023−232-22-200−1+31−3−1−31+3−1−31+3−1+31−30000000000000000000000
χ524-4-4400-24-42-22000000023−23-220023−23-22-22001−3−1+31+3−1−31+3−1−31−3−1+30000000000000000000000
χ534-4-4400-24-42-220000000−2323-2200−23232-22-200−1−31+3−1+31−3−1+31−3−1−31+30000000000000000000000
χ544-4-4400-24-42-220000000−2323-2200−2323-22-22001+3−1−31−3−1+31−3−1+31+3−1−30000000000000000000000
χ554-4-4400-2-442-22000000023−232-200−23232-2-2200−1−31+31−3−1+3−1+31−31+3−1−30000000000000000000000
χ564-4-4400-2-442-22000000023−232-200−2323-222-2001+3−1−3−1+31−31−3−1+3−1−31+30000000000000000000000
χ574-4-4400-2-442-220000000−23232-20023−232-2-2200−1+31−31+3−1−3−1−31+31−3−1+30000000000000000000000
χ584-4-4400-2-442-220000000−23232-20023−23-222-2001−3−1+3−1−31+31+3−1−3−1+31−30000000000000000000000
χ5988-8-88-8-400-44400000-4400000000000000000000000000000000000000000000
χ6088-8-8-88-400-444000004-400000000000000000000000000000000000000000000
χ618-88-800800-8-88000000000000000000000000000000000000000000000000000
χ628-88-800-40044-40000000000043−4300000000000000000000000000000000000000
χ638-88-800-40044-400000000000−434300000000000000000000000000000000000000

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