Finite Group Databasebeta

← Group #10707625

Character table — Group #10707625

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size11112222224444888888888888881616161616161616161616161616164848484848484848
order12222236664466444412121212121212121212488881212242424242424242424444488
χ1111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111
χ411111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111111111-1-11111-1-1-1-11111-111-1-1-1-11111-1-1-1-1111-11-1-1-1
χ611111111111111-1-11111-1-1-1-11111-111-1-1-1-11111-1-1-1-1-1-1-11-1111
χ711111111111111-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-1111111-11-11-1-1
χ811111111111111-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-11111-1-11-11-111
χ92222222222222222-2-2222222-2-2-2-2-20000-2-20000000000000000
χ1022222222222222-2-2-2-222-2-2-2-2-2-2-2-220000220000000000000000
χ112222222222-2-222002-2-2-2000022-2-20000000000000000020-2000
χ122222222222-2-222002-2-2-2000022-2-200000000000000000-202000
χ132222222222-2-22200-22-2-20000-2-22200000000000000000020-200
χ142222222222-2-22200-22-2-20000-2-222000000000000000000-20200
χ15222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-100000000
χ16222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-12-2-2-2-2-1-11111111100000000
χ17222222-1-1-1-122-1-122-2-2-1-1-1-1-1-11111-200001133−3−333−3−300000000
χ18222222-1-1-1-122-1-122-2-2-1-1-1-1-1-11111-2000011−3−333−3−33300000000
χ19222222-1-1-1-122-1-1-2-222-1-11111-1-1-1-1-222-2-211-1-1-1-1111100000000
χ20222222-1-1-1-122-1-1-2-222-1-11111-1-1-1-1-2-2-222111111-1-1-1-100000000
χ21222222-1-1-1-122-1-1-2-2-2-2-1-11111111120000-1-133−3−3−3−33300000000
χ22222222-1-1-1-122-1-1-2-2-2-2-1-11111111120000-1-1−3−33333−3−300000000
χ232-2-22-2222-2-2-22-222-2002-222-2-2000002−22−2002−22−22−22−200000000
χ242-2-22-2222-2-2-22-222-2002-222-2-200000−22−2200−22−22−22−2200000000
χ252-2-22-2222-2-2-22-22-22002-2-2-222000002−2−22002−22−2−22−2200000000
χ262-2-22-2222-2-2-22-22-22002-2-2-22200000−222−200−22−222−22−200000000
χ272-2-22-22-1-111-221-12-200-11-1-1113−33−302−22−23−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ282-2-22-22-1-111-221-12-200-11-1-1113−33−30−22−223−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ292-2-22-22-1-111-221-12-200-11-1-111−33−3302−22−2−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ302-2-22-22-1-111-221-12-200-11-1-111−33−330−22−22−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ312-2-22-22-1-111-221-1-2200-1111-1-13−33−302−2−22−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ322-2-22-22-1-111-221-1-2200-1111-1-13−33−30−222−2−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ332-2-22-22-1-111-221-1-2200-1111-1-1−33−3302−2−223−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ342-2-22-22-1-111-221-1-2200-1111-1-1−33−330−222−23−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ35444444-2-2-2-2-4-4-2-2004-4220000-2-22200000000000000000000000
χ36444444-2-2-2-2-4-4-2-200-4422000022-2-200000000000000000000000
χ374444-4-4444400-4-4000000000000000000000000000002-2000000
χ384444-4-4444400-4-400000000000000000000000000000-22000000
χ394-4-444-444-4-4004-4000000000000000000000000000000000002i−2i
χ404-4-444-444-4-4004-400000000000000000000000000000000000−2i2i
χ414-4-44-4444-4-44-4-440000-440000000000000000000000000000000
χ424-4-44-44-2-2224-42-200002-2000023−23−232300000000000000000000000
χ434-4-44-44-2-2224-42-200002-20000−232323−2300000000000000000000000
χ448888-8-8-4-4-4-400440000000000000000000000000000000000000
χ4588-8-8008-88-800000000000000000000000000000000000000000
χ4688-8-800-44-44000000000023−2323−23000000000000000000000000000
χ4788-8-800-44-440000000000−2323−2323000000000000000000000000000
χ488-88-8008-8-8800000000000000000000000000000000000000000
χ498-88-800-444-4000000000023−23−2323000000000000000000000000000
χ508-88-800-444-40000000000−232323−23000000000000000000000000000
χ518-8-888-8-4-44400-440000000000000000000000000000000000000

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