Finite Group Databasebeta

← Group #10770153

Character table — Group #10770153

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444888888888888888888161616161616161616162424242424242424242424244848
order1222223446662244466661212121212122444688881224242424242424246881212122424242424444444444424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1
χ6111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-11111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-111-1111111-1-1
χ91111111-1-1111-1-1-11111-1-1-1-1111111-1-1-111-1-1-11111-1-1-1-111-11-1-111-1-111-11-1-11-111-1-11-1
χ101111111-1-1111-1-1-11111-1-1-1-1111111-1-1-111-1-1-11111-1-1-1-111-11-1-111-1-1-1-11-111-11-1-111-11
χ111111111-1-1111-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-111111-111-1-1-1-11111-11-1-11-1-1-111-11
χ121111111-1-1111-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-1-1-111111-111-1-1-1-111-1-11-111-1111-1-11-1
χ131111111-1-1111-1-1-11111-1-1-1-11111-1-111-111-1-1-11111-1-1-1-1-1-11-111-1-11111-1-11-1-1111-1-1-11
χ141111111-1-1111-1-1-11111-1-1-1-11111-1-111-111-1-1-11111-1-1-1-1-1-11-111-1-111-1-111-111-1-1-1111-1
χ151111111-1-1111-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1-1-1-11111-11-1-11111-1-111-1-11-1-11-1-1111-1
χ161111111-1-1111-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1-1-1-11111-11-1-11111-1-1-1-111-111-111-1-1-11
χ17222222222222-2-22-2-222-2-222-2-2-2-22-22-2-20000200000000200-22-2000000000000000000
χ18222222222222-2-22-2-222-2-222-2-2-2-2-22-22-20000200000000-2002-22000000000000000000
χ192222222-2-222222-2-2-22222-2-2-2-2-2-22-2-2220000-200000000200-2-22000000000000000000
χ202222222-2-222222-2-2-22222-2-2-2-2-2-2-222-220000-200000000-20022-2000000000000000000
χ21222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-100000000000000
χ22222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-111111111-1-2-2-1-1-1111100000000000000
χ23222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-11-2-2111111100000000000000
χ24222222-122-1-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-111111111122111-1-1-1-100000000000000
χ25222222-122-1-1-1-2-22-2-2-1-111-1-111112-22-210000-133−3−333−3−3-1001-113−33−300000000000000
χ26222222-122-1-1-1-2-22-2-2-1-111-1-111112-22-210000-1−3−333−3−333-1001-11−33−3300000000000000
χ27222222-122-1-1-1-2-22-2-2-1-111-1-11111-22-2210000-133−3−333−3−3100-11-1−33−3300000000000000
χ28222222-122-1-1-1-2-22-2-2-1-111-1-11111-22-2210000-1−3−333−3−333100-11-13−33−300000000000000
χ29222222-1-2-2-1-1-122-2-2-2-1-1-1-11111112-2-22-10000133−3−3−3−333-10011-13−3−3300000000000000
χ30222222-1-2-2-1-1-122-2-2-2-1-1-1-11111112-2-22-100001−3−33333−3−3-10011-1−333−300000000000000
χ31222222-1-2-2-1-1-122-2-2-2-1-1-1-1111111-222-2-10000133−3−3−3−333100-1-11−333−300000000000000
χ32222222-1-2-2-1-1-122-2-2-2-1-1-1-1111111-222-2-100001−3−33333−3−3100-1-113−3−3300000000000000
χ33222222-1-2-2-1-1-1-2-2-222-1-11111-1-1-1-122-2-2122-2-21-1-1-1-11111-12-2-111-1-11100000000000000
χ34222222-1-2-2-1-1-1-2-2-222-1-11111-1-1-1-122-2-21-2-22211111-1-1-1-1-1-22-11111-1-100000000000000
χ35222222-1-2-2-1-1-1-2-2-222-1-11111-1-1-1-1-2-222122-2-21-1-1-1-111111-221-1-111-1-100000000000000
χ36222222-1-2-2-1-1-1-2-2-222-1-11111-1-1-1-1-2-2221-2-22211111-1-1-1-112-21-1-1-1-11100000000000000
χ372222-2-22222222-2-22-2-2-2222222-2-20000-20000-20000000000000000000002-20-22000000
χ382222-2-22222222-2-22-2-2-2222222-2-20000-20000-2000000000000000000000-2202-2000000
χ392222-2-2222222-22-2-22-2-2-2-222-2-222000020000-20000000000000000002-2-200200000000
χ402222-2-2222222-22-2-22-2-2-2-222-2-222000020000-2000000000000000000-22200-200000000
χ412222-2-22-2-22222-22-22-2-222-2-2-2-2220000-2000020000000000000000002-2200-200000000
χ422222-2-22-2-22222-22-22-2-222-2-2-2-2220000-200002000000000000000000-22-200200000000
χ432222-2-22-2-2222-2222-2-2-2-2-2-2-222-2-20000200002000000000000000000000220-2-2000000
χ442222-2-22-2-2222-2222-2-2-2-2-2-2-222-2-20000200002000000000000000000000-2-2022000000
χ454444-4-4-244-2-2-24-4-44-422-2-2-2-2-2-222000020000200000000000000000000000000000000
χ464444-4-4-244-2-2-2-44-4-442222-2-222-2-20000-20000200000000000000000000000000000000
χ474444-4-4-2-4-4-2-2-24-44-4422-2-22222-2-2000020000-200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-2-4444-4222222-2-2220000-20000-200000000000000000000000000000000
χ4944-4-40044i−4i4-4-40000000004i−4i00000000000000000000000000000000000000002-22i−2i00
χ5044-4-40044i−4i4-4-40000000004i−4i0000000000000000000000000000000000000000-22−2i2i00
χ5144-4-4004−4i4i4-4-4000000000−4i4i00000000000000000000000000000000000000002-2−2i2i00
χ5244-4-4004−4i4i4-4-4000000000−4i4i0000000000000000000000000000000000000000-222i−2i00
χ534-44-44-4400-44-4000004-4000000000000000−2i22i200000−2i22i2−2i22i2000000000000000000000000
χ544-44-44-4400-44-4000004-40000000000000002i2−2i2000002i2−2i22i2−2i2000000000000000000000000
χ554-44-44-4-2002-2200000-22000023−2323−230000000−2i22i2000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000
χ564-44-44-4-2002-2200000-22000023−2323−2300000002i2−2i200000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000
χ574-44-44-4-2002-2200000-220000−2323−23230000000−2i22i2000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000
χ584-44-44-4-2002-2200000-220000−2323−232300000002i2−2i200000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000
χ594-44-4-44400-44-400000-440000000000000−2i22i2000−2i22i2−2i22i20000000000000000000000000000
χ604-44-4-44400-44-400000-4400000000000002i2−2i20002i2−2i22i2−2i20000000000000000000000000000
χ614-44-4-44-2002-22000002-2000023−23−232300000−2i22i20002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000
χ624-44-4-44-2002-22000002-2000023−23−2323000002i2−2i2000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000
χ634-44-4-44-2002-22000002-20000−232323−2300000−2i22i20002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000
χ644-44-4-44-2002-22000002-20000−232323−23000002i2−2i2000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ230000000000000000000000000000
χ6588-8-800-48i−8i-444000000000−4i4i0000000000000000000000000000000000000000000000
χ6688-8-800-4−8i8i-4440000000004i−4i0000000000000000000000000000000000000000000000
χ678-8-8800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-8-8800-40044-40000000−4i34i3000000000000000000000000000000000000000000000000
χ698-8-8800-40044-400000004i3−4i3000000000000000000000000000000000000000000000000

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