Finite Group Databasebeta

← Group #10949938

Character table — Group #10949938

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222222222222244444444444444444448888888888888888888888888888888888242424242424242448484848
order12222344446881212242424246668888888121212242424242424441212121216161616161616162424242448484848484848484848484848484848224488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911-1-111-1-111111111111-1-111-1-111-1-1-1-1111-1-1-1-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-11-11-1
χ1011-1-111-1-111111111111-1-111-1-111-1-1-1-1111-1-1-1-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-11-11
χ1111-1-111-1-111111111111-1-111-1-111-1-1-1-1111-1-1-1-11-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-11-11
χ1211-1-111-1-111111111111-1-111-1-111-1-1-1-1111-1-1-1-11-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-11-1
χ1311-1-111-1-111111111111-1-111-1-1-1-111-1-1111-1-1-1-1-11-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-1111-1-11
χ1411-1-111-1-111111111111-1-111-1-1-1-111-1-1111-1-1-1-1-11-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-11-1111-1-1-111-1
χ1511-1-111-1-111111111111-1-111-1-1-1-111-1-1111-1-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11-11-1-1-111-111-1
χ1611-1-111-1-111111111111-1-111-1-1-1-111-1-1111-1-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1111-1-11-1-11
χ1722222222222-2-222-2-2-2-2222-2-2-22222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000
χ1822222222222-2-222-2-2-2-2222-2-2-2-2-2-2-2222-2-2-2-2-2-222222200000000-2-2-2-20000000000000000000000000000
χ1922222-12222-122-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2022222-12222-122-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111000000000000
χ2122222-12222-122-1-1-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-111111111000000000000
χ2222222-12222-122-1-1-1-1-1-1-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-1000000000000
χ2322222-12222-1-2-2-1-11111-1-1-1-2-2-22222-1-1-1111111-2-2111100000000-1-1-1-133−3−333−3−333−3−333−3−3000000000000
χ2422222-12222-1-2-2-1-11111-1-1-1-2-2-22222-1-1-1111111-2-2111100000000-1-1-1-1−3−333−3−333−3−333−3−333000000000000
χ2522222-12222-1-2-2-1-11111-1-1-1-2-2-2-2-2-2-2-1-1-111111122-1-1-1-100000000111133−3−333−3−3−3−333−3−333000000000000
χ2622222-12222-1-2-2-1-11111-1-1-1-2-2-2-2-2-2-2-1-1-111111122-1-1-1-1000000001111−3−333−3−33333−3−333−3−3000000000000
χ27222-2-222-22-22222222222-2-2-22-200002-2-2-2-222-2-2000000000000000000000000000000000000002i−2i2i−2i0000
χ28222-2-222-22-22222222222-2-2-22-200002-2-2-2-222-2-200000000000000000000000000000000000000−2i2i−2i2i0000
χ29222-2-222-22-22-2-222-2-2-2-22-2-22-2200002-2-222-2-222000000000000000000000000000000000022-2-200000000
χ30222-2-222-22-22-2-222-2-2-2-22-2-22-2200002-2-222-2-2220000000000000000000000000000000000-2-22200000000
χ31222-2-22-22-22200-2-200002-2-20002-22-2-222000000000000−i2i2−i2i2−i2i2−i2i22-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ32222-2-22-22-22200-2-200002-2-20002-22-2-222000000000000i2−i2i2−i2i2−i2i2−i22-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ33222-2-22-22-22200-2-200002-2-2000-22-22-222000000000000−i2i2−i2i2i2−i2i2−i2-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ34222-2-22-22-22200-2-200002-2-2000-22-22-222000000000000i2−i2i2−i2−i2i2−i2i2-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ35222-2-2-1-22-22-1001133−3−3-1110002-22-21-1-13−33−33−3003−33−3−i2i2−i2i2−i2i2−i2i2-11-11ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ36222-2-2-1-22-22-1001133−3−3-1110002-22-21-1-13−33−33−3003−33−3i2−i2i2−i2i2−i2i2−i2-11-11−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ37222-2-2-1-22-22-1001133−3−3-111000-22-221-1-13−33−33−300−33−33−i2i2−i2i2i2−i2i2−i21-11-1ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ38222-2-2-1-22-22-1001133−3−3-111000-22-221-1-13−33−33−300−33−33i2−i2i2−i2−i2i2−i2i21-11-1−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ39222-2-2-1-22-22-10011−3−333-1110002-22-21-1-1−33−33−3300−33−33−i2i2−i2i2−i2i2−i2i2-11-11ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ40222-2-2-1-22-22-10011−3−333-1110002-22-21-1-1−33−33−3300−33−33i2−i2i2−i2i2−i2i2−i2-11-11−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ41222-2-2-1-22-22-10011−3−333-111000-22-221-1-1−33−33−33003−33−3−i2i2−i2i2i2−i2i2−i21-11-1ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ42222-2-2-1-22-22-10011−3−333-111000-22-221-1-1−33−33−33003−33−3i2−i2i2−i2−i2i2−i2i21-11-1−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ4322-22-222-2-22200-2-20000-22-20002-2-222-22000000000000−i2i2i2−i2−i2i2i2−i22-2-22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-22-222-2-22200-2-20000-22-20002-2-222-22000000000000i2−i2−i2i2i2−i2−i2i22-2-22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-22-222-2-22200-2-20000-22-2000-222-22-22000000000000−i2i2i2−i2i2−i2−i2i2-222-2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4622-22-222-2-22200-2-20000-22-2000-222-22-22000000000000i2−i2−i2i2−i2i2i2−i2-222-2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4722-22-22-222-2222222222-22-2-2-220000-22-2-2-2-2-222000000000000000000000000000000000000002i−2i−2i2i0000
χ4822-22-22-222-2222222222-22-2-2-220000-22-2-2-2-2-22200000000000000000000000000000000000000−2i2i2i−2i0000
χ4922-22-22-222-22-2-222-2-2-2-2-22-222-20000-22-22222-2-200000000000000000000000000000000002-2-2200000000
χ5022-22-22-222-22-2-222-2-2-2-2-22-222-20000-22-22222-2-20000000000000000000000000000000000-222-200000000
χ5122-22-2-12-2-22-1001133−3−31-110002-2-22-11-13−3−33−33003−3−33−i2i2i2−i2−i2i2i2−i2-111-1ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5222-22-2-12-2-22-1001133−3−31-110002-2-22-11-13−3−33−33003−3−33i2−i2−i2i2i2−i2−i2i2-111-1−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5322-22-2-12-2-22-1001133−3−31-11000-222-2-11-13−3−33−3300−333−3−i2i2i2−i2i2−i2−i2i21-1-11ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5422-22-2-12-2-22-1001133−3−31-11000-222-2-11-13−3−33−3300−333−3i2−i2−i2i2−i2i2i2−i21-1-11−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5522-22-2-12-2-22-10011−3−3331-110002-2-22-11-1−333−33−300−333−3−i2i2i2−i2−i2i2i2−i2-111-1ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5622-22-2-12-2-22-10011−3−3331-110002-2-22-11-1−333−33−300−333−3i2−i2−i2i2i2−i2−i2i2-111-1−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5722-22-2-12-2-22-10011−3−3331-11000-222-2-11-1−333−33−3003−3−33−i2i2i2−i2i2−i2−i2i21-1-11ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5822-22-2-12-2-22-10011−3−3331-11000-222-2-11-1−333−33−3003−3−33i2−i2−i2i2−i2i2i2−i21-1-11−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5922-2-222-2-2222-2-222-2-2-2-2-2-22-22222-2-2-2-22-2-22222-22-2-2220000000022-2-20000000000000000000000000000
χ6022-2-222-2-2222-2-222-2-2-2-2-2-22-222-2-222-2-22-2-222222-222-2-200000000-2-2220000000000000000000000000000
χ6122-2-22-1-2-222-122-1-1-1-1-1-111-12-2-222-2-211-1-1-111112-2-1-11122-2-222-2-2-1-111-1-1-1-11111-1-1-1-11111000000000000
χ6222-2-22-1-2-222-122-1-1-1-1-1-111-12-2-222-2-211-1-1-111112-2-1-111-2-222-2-222-1-1111111-1-1-1-11111-1-1-1-1000000000000
χ6322-2-22-1-2-222-122-1-1-1-1-1-111-12-2-2-2-22211-1-1-11111-2211-1-122-2-2-2-22211-1-1-1-1-1-111111111-1-1-1-1000000000000
χ6422-2-22-1-2-222-122-1-1-1-1-1-111-12-2-2-2-22211-1-1-11111-2211-1-1-2-22222-2-211-1-11111-1-1-1-1-1-1-1-11111000000000000
χ6522-2-22-1-2-222-1-2-2-1-1111111-1-22222-2-211-111-1-1-1-1-2211-1-100000000-1-11133−3−3−3−33333−3−3−3−333000000000000
χ6622-2-22-1-2-222-1-2-2-1-1111111-1-22222-2-211-111-1-1-1-1-2211-1-100000000-1-111−3−33333−3−3−3−33333−3−3000000000000
χ6722-2-22-1-2-222-1-2-2-1-1111111-1-222-2-22211-111-1-1-1-12-2-1-1110000000011-1-133−3−3−3−333−3−33333−3−3000000000000
χ6822-2-22-1-2-222-1-2-2-1-1111111-1-222-2-22211-111-1-1-1-12-2-1-1110000000011-1-1−3−33333−3−333−3−3−3−333000000000000
χ69444444-4-4-4-4400-4-400004440000000-4-4-40000000000000000000000000000000000000000000000000000
χ7044444-2-4-4-4-4-200222323−23−23-2-2-20000000222−232323−23−23230000000000000000000000000000000000000000000000
χ7144444-2-4-4-4-4-20022−23−232323-2-2-2000000022223−23−232323−230000000000000000000000000000000000000000000000
χ72444-4-4-24-44-4-244-2-2-2-2-2-2-222-44-40000-22222-2-2220000000000000000000000000000000000000000000000
χ73444-4-4-24-44-4-2-4-4-2-22222-2224-440000-222-2-222-2-20000000000000000000000000000000000000000000000
χ7444-44-4-2-444-4-244-2-2-2-2-2-22-22-4-4400002-222222-2-20000000000000000000000000000000000000000000000
χ7544-44-4-2-444-4-2-4-4-2-222222-2244-400002-22-2-2-2-2220000000000000000000000000000000000000000000000
χ7644-4-44444-4-4400-4-40000-4-44000000044-40000000000000000000000000000000000000000000000000000
χ7744-4-44-244-4-4-200222323−23−2322-20000000-2-22−2323−232323−230000000000000000000000000000000000000000000000
χ7844-4-44-244-4-4-20022−23−23232322-20000000-2-2223−2323−23−23230000000000000000000000000000000000000000000000
χ798-800080000-8−4i24i200−4i24i2−4i24i200000000000000000000000000000000000000000000000000000000000000000
χ808-800080000-84i2−4i2004i2−4i24i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ818-8000-400004−4i24i243−434ζ5+4ζ7−4ζ5−4ζ74ζ13+4ζ23−4ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000000000
χ828-8000-400004−4i24i2−43434ζ13+4ζ23−4ζ13−4ζ234ζ5+4ζ7−4ζ5−4ζ700000000000000000000000000000000000000000000000000000000000000000
χ838-8000-4000044i2−4i243−43−4ζ5−4ζ74ζ5+4ζ7−4ζ13−4ζ234ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000000000
χ848-8000-4000044i2−4i2−4343−4ζ13−4ζ234ζ13+4ζ23−4ζ5−4ζ74ζ5+4ζ700000000000000000000000000000000000000000000000000000000000000000

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