Finite Group Databasebeta

← Group #10696817

Character table — Group #10696817

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222224444444444444448888888888888816161616161616161616161624242424484848484848
order122222344666444446612121212121212128888121224242424242424242466881212242424248888224488
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
χ5111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1
χ6111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ8111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ9222222222222-2-2-2-2222-2-222-2-2-2-20000-22000000002-22200-2-200000000000000
χ10222222222222-2-2-2-2222-2-222-2-2-2-20000-2200000000-22-2-2002200000000000000
χ112222222-2-222222-2-2-22222-2-2-2-2-2-200002-20000000000002i−2i002i2i−2i−2i0000000000
χ122222222-2-222222-2-2-22222-2-2-2-2-2-200002-2000000000000−2i2i00−2i−2i2i2i0000000000
χ132222222-2-2222-2-222-222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000
χ142222222-2-2222-2-222-222-2-2-2-22222-2-222-2-2-2-2-2-222220000000000000000000000
χ15222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-10000000000
χ16222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-21111110000000000
χ17222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-111110000000000
χ18222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-10000000000
χ19222222-122-1-1-1-2-2-2-22-1-111-1-1111100001-133−3−333−3−32-2-1-100113−33−30000000000
χ20222222-122-1-1-1-2-2-2-22-1-111-1-1111100001-133−3−333−3−3-221100-1-1−33−330000000000
χ21222222-122-1-1-1-2-2-2-22-1-111-1-1111100001-1−3−333−3−3332-2-1-10011−33−330000000000
χ22222222-122-1-1-1-2-2-2-22-1-111-1-1111100001-1−3−333−3−333-221100-1-13−33−30000000000
χ23222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-1133−3−3−3−33300−i3i32i−2i−i3i3−i−iii0000000000
χ24222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-1133−3−3−3−33300i3−i3−2i2ii3−i3ii−i−i0000000000
χ25222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-11−3−33333−3−300−i3i3−2i2i−i3i3ii−i−i0000000000
χ26222222-1-2-2-1-1-122-2-2-2-1-1-1-11111110000-11−3−33333−3−300i3−i32i−2ii3−i3−i−iii0000000000
χ27222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-122-2-211-1-1-1-1111100−i3i300i3−i3−i3i3i3−i30000000000
χ28222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-122-2-211-1-1-1-1111100i3−i300−i3i3i3−i3−i3i30000000000
χ29222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-1-2-222111111-1-1-1-100−i3i300i3−i3i3−i3−i3i30000000000
χ30222222-1-2-2-1-1-1-2-222-2-1-11111-1-1-1-1-2-222111111-1-1-1-100i3−i300−i3i3−i3i3i3−i30000000000
χ312222-2-22222222-22-2-2-2-2222222-2-20000-2-2000000000000000000000000002-200
χ322222-2-22222222-22-2-2-2-2222222-2-20000-2-200000000000000000000000000-2200
χ332222-2-2222222-22-22-2-2-2-2-222-2-22200002-200000000000000000000000000002-2
χ342222-2-2222222-22-22-2-2-2-2-222-2-22200002-20000000000000000000000000000-22
χ352222-2-22-2-22222-2-222-2-222-2-2-2-2220000-220000000000000000000022-2-2000000
χ362222-2-22-2-22222-2-222-2-222-2-2-2-2220000-2200000000000000000000-2-222000000
χ372222-2-22-2-2222-222-22-2-2-2-2-2-222-2-20000220000000000000000000000002-20000
χ382222-2-22-2-2222-222-22-2-2-2-2-2-222-2-2000022000000000000000000000000-220000
χ394444-4-4-244-2-2-24-44-4-422-2-2-2-2-2-222000022000000000000000000000000000000
χ404444-4-4-244-2-2-2-44-44-42222-2-222-2-20000-22000000000000000000000000000000
χ414444-4-4-2-4-4-2-2-24-4-44422-2-22222-2-200002-2000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-2-444-44222222-2-2220000-2-2000000000000000000000000000000
χ4344-4-44-44004-4-4000004-40000000000−2i22i2000000−2i22i2−2i22i20000000000000000000000
χ4444-4-44-44004-4-4000004-400000000002i2−2i20000002i2−2i22i2−2i20000000000000000000000
χ4544-4-44-4-200-22200000-22000023−2323−2300−2i22i20000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ230000000000000000000000
χ4644-4-44-4-200-22200000-22000023−2323−23002i2−2i2000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ230000000000000000000000
χ4744-4-44-4-200-22200000-220000−2323−232300−2i22i20000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000000000
χ4844-4-44-4-200-22200000-220000−2323−2323002i2−2i2000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000000000
χ4944-4-4-444004-4-400000-4400000000−2i22i20000−2i22i2−2i22i200000000000000000000000000
χ5044-4-4-444004-4-400000-44000000002i2−2i200002i2−2i22i2−2i200000000000000000000000000
χ5144-4-4-44-200-222000002-2000023−23−2323−2i22i200002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ5244-4-4-44-200-222000002-2000023−23−23232i2−2i20000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ5344-4-4-44-200-222000002-20000−232323−23−2i22i200002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ5444-4-4-44-200-222000002-20000−232323−232i2−2i20000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ554-4-440044-4-4-440000000004-40000000000000000000000000000002-22-2000000
χ564-4-440044-4-4-440000000004-4000000000000000000000000000000-22-22000000
χ574-4-44004-44-4-44000000000-440000000000000000000000000000002-2-22000000
χ584-4-44004-44-4-44000000000-44000000000000000000000000000000-222-2000000
χ598-88-800800-88-8000000000000000000000000000000000000000000000000000
χ608-88-800-4004-44000000043−43000000000000000000000000000000000000000000
χ618-88-800-4004-440000000−4343000000000000000000000000000000000000000000
χ628-8-8800-48-844-4000000000-440000000000000000000000000000000000000000
χ638-8-8800-4-8844-40000000004-40000000000000000000000000000000000000000

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