Finite Group Databasebeta

← Group #10691957

Character table — Group #10691957

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222234444446661212121244466888888881212121212128888121224242424242424242424242424242424222244448888888888242424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111
χ91111-1-111-11-1-1-111111111-11-1-1iiii−i−i−i−i-1-1-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-111-1-11-1i−i
χ101111-1-111-11-1-1-111111111-11-1-1iiii−i−i−i−i-1-1-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−i−i−iiiii1-111-1-1-11−ii
χ111111-1-111-11-1-1-111111111-11-1-1iiii−i−i−i−i-1-1-1-1-1-1−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1iiii−i−i−i−i-11-1-111-11−ii
χ121111-1-111-11-1-1-111111111-11-1-1iiii−i−i−i−i-1-1-1-1-1-1−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−i−i−iiiii-11-1-1111-1i−i
χ131111-1-111-11-1-1-111111111-11-1-1−i−i−i−iiiii-1-1-1-1-1-1ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−i−i−iiiii-11-1-111-11i−i
χ141111-1-111-11-1-1-111111111-11-1-1−i−i−i−iiiii-1-1-1-1-1-1ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111iiii−i−i−i−i-11-1-1111-1−ii
χ151111-1-111-11-1-1-111111111-11-1-1−i−i−i−iiiii-1-1-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii1-111-1-11-1−ii
χ161111-1-111-11-1-1-111111111-11-1-1−i−i−i−iiiii-1-1-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i1-111-1-1-11i−i
χ1722222222222-2-22222222-2-2-222000000002-2-2-2-220000-2-200000000000000002222-2-2-2-2000000000000000000
χ1822222222222-2-22222222-2-2-222000000002-2-2-2-220000-2-20000000000000000-2-2-2-22222000000000000000000
χ192222222-2-2-2-222222-2-2-2-2-2-222222-2-222-2-2-2-2-222-200002-222-2-222-2-20000000000000000000000000000000000
χ202222222-2-2-2-222222-2-2-2-2-2-2222-2-222-2-222-2-2-222-200002-2-2-222-2-2220000000000000000000000000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-222-22200000000-222-2-2-20000-220000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ222222222-2-2-2-2-2-2222-2-2-2-222-22200000000-222-2-2-20000-22000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ24222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ27222222-1-2-2-2-222-1-1-11111-2-22-1-122-2-222-2-2111-1-110000-11-1-111-1-11133−3−333−3−30000000000000000003−33−30000
χ28222222-1-2-2-2-222-1-1-11111-2-22-1-122-2-222-2-2111-1-110000-11-1-111-1-111−3−333−3−333000000000000000000−33−330000
χ29222222-1-2-2-2-222-1-1-11111-2-22-1-1-2-222-2-222111-1-110000-1111-1-111-1-133−3−333−3−3000000000000000000−33−330000
χ30222222-1-2-2-2-222-1-1-11111-2-22-1-1-2-222-2-222111-1-110000-1111-1-111-1-1−3−333−3−3330000000000000000003−33−30000
χ312222-2-222-22-2222222222-22-2-2-200000000-22222-20000-2-2000000000000000022-2-2-2-222000000000000000000
χ322222-2-222-22-2222222222-22-2-2-200000000-22222-20000-2-20000000000000000-2-22222-2-2000000000000000000
χ332222-2-22-22-2222222-2-2-2-22-2-2-2-2000000002-2-22220000-2200000000000000000000000022-2-2-2-2220000000000
χ342222-2-22-22-2222222-2-2-2-22-2-2-2-2000000002-2-22220000-22000000000000000000000000-2-22222-2-20000000000
χ352222-2-22-22-22-2-2222-2-2-2-2-222-2-22i2i−2i−2i−2i−2i2i2i222-2-2200002-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ362222-2-22-22-22-2-2222-2-2-2-2-222-2-2−2i−2i2i2i2i2i−2i−2i222-2-2200002-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ372222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-22112i2i2i2i−2i−2i−2i−2i1111112i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii00000000000000002-2-1-1110000
χ382222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-22112i2i2i2i−2i−2i−2i−2i111111−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000-2211-1-10000
χ392222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-2211−2i−2i−2i−2i2i2i2i2i1111112i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000-2211-1-10000
χ402222-2-2-12-22-2-2-2-1-1-1-1-1-1-12-2211−2i−2i−2i−2i2i2i2i2i111111−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i00000000000000002-2-1-1110000
χ412222-2-2-1-22-22-2-2-1-1-11111-222112i2i−2i−2i−2i−2i2i2i-1-1-111-10000-11−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000000000000000−333−30000
χ422222-2-2-1-22-22-2-2-1-1-11111-222112i2i−2i−2i−2i−2i2i2i-1-1-111-10000-11−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000000000000000003−3−330000
χ432222-2-2-1-22-22-2-2-1-1-11111-22211−2i−2i2i2i2i2i−2i−2i-1-1-111-10000-11ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000000000000000003−3−330000
χ442222-2-2-1-22-22-2-2-1-1-11111-22211−2i−2i2i2i2i2i−2i−2i-1-1-111-10000-11ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000000000000000−333−30000
χ452-22-22-222-2-22002-2-222-2-20002-2−i2i2−i2i2−i2i2−i2i2-200002000000−i2i2−i2i2−i2i2−i2i20000000000002i−2i2i−2i2−22−22−22−20000000000
χ462-22-22-222-2-22002-2-222-2-20002-2−i2i2−i2i2−i2i2−i2i2-200002000000−i2i2−i2i2−i2i2−i2i2000000000000−2i2i−2i2i−22−22−22−220000000000
χ472-22-22-222-2-22002-2-222-2-20002-2i2−i2i2−i2i2−i2i2−i2-200002000000i2−i2i2−i2i2−i2i2−i20000000000002i−2i2i−2i−22−22−22−220000000000
χ482-22-22-222-2-22002-2-222-2-20002-2i2−i2i2−i2i2−i2i2−i2-200002000000i2−i2i2−i2i2−i2i2−i2000000000000−2i2i−2i2i2−22−22−22−20000000000
χ492-22-22-22-222-2002-2-2-2-2220002-2−i2i2i2−i2−i2i2i2−i220000-2000000−i2i2i2−i2−i2i2i2−i2000000002-22-20000−i2i2i2−i2−i2i2i2−i20000000000
χ502-22-22-22-222-2002-2-2-2-2220002-2−i2i2i2−i2−i2i2i2−i220000-2000000−i2i2i2−i2−i2i2i2−i200000000-22-220000i2−i2−i2i2i2−i2−i2i20000000000
χ512-22-22-22-222-2002-2-2-2-2220002-2i2−i2−i2i2i2−i2−i2i220000-2000000i2−i2−i2i2i2−i2−i2i2000000002-22-20000i2−i2−i2i2i2−i2−i2i20000000000
χ522-22-22-22-222-2002-2-2-2-2220002-2i2−i2−i2i2i2−i2−i2i220000-2000000i2−i2−i2i2i2−i2−i2i200000000-22-220000−i2i2i2−i2−i2i2i2−i20000000000
χ532-22-2-22222-2-2002-2-222-2-2000-222−22−2−22−2220000-20000002−22−2−22−220000000000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i20000000000
χ542-22-2-22222-2-2002-2-222-2-2000-222−22−2−22−2220000-20000002−22−2−22−22000000000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i20000000000
χ552-22-2-22222-2-2002-2-222-2-2000-22−22−222−22−220000-2000000−22−222−22−20000000000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i20000000000
χ562-22-2-22222-2-2002-2-222-2-2000-22−22−222−22−220000-2000000−22−222−22−2000000000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i20000000000
χ572-22-2-222-2-222002-2-2-2-222000-222−2−22−222−2-2000020000002−2−22−222−2000000002-2-2200002−2−22−222−20000000000
χ582-22-2-222-2-222002-2-2-2-222000-222−2−22−222−2-2000020000002−2−22−222−200000000-222-20000−222−22−2−220000000000
χ592-22-2-222-2-222002-2-2-2-222000-22−222−22−2−22-200002000000−222−22−2−22000000002-2-220000−222−22−2−220000000000
χ602-22-2-222-2-222002-2-2-2-222000-22−222−22−2−22-200002000000−222−22−2−2200000000-222-200002−2−22−222−20000000000
χ61444444-24444-4-4-2-2-2-2-2-2-2-4-4-4-2-200000000-22222-2000022000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-4-4-2-2-2222244-4-2-2000000002-2-222200002-2000000000000000000000000000000000000000000
χ634444-4-4-24-44-444-2-2-2-2-2-2-2-44-422000000002-2-2-2-22000022000000000000000000000000000000000000000000
χ644444-4-4-2-44-4444-2-2-222224-4-42200000000-222-2-2-200002-2000000000000000000000000000000000000000000
χ6544-4-400400004i−4i-44-4000000000000000000004i−4i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ6644-4-400400004i−4i-44-4000000000000000000004i−4i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ6744-4-40040000−4i4i-44-400000000000000000000−4i4i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ6844-4-40040000−4i4i-44-400000000000000000000−4i4i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ6944-4-400-200004i−4i2-2223−2323−2300000000000000−2i32i3−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000000000
χ7044-4-400-200004i−4i2-2223−2323−2300000000000000−2i32i3−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000000000
χ7144-4-400-200004i−4i2-22−2323−2323000000000000002i3−2i3−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000000000
χ7244-4-400-200004i−4i2-22−2323−2323000000000000002i3−2i3−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000000000
χ7344-4-400-20000−4i4i2-2223−2323−23000000000000002i3−2i32i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000000000
χ7444-4-400-20000−4i4i2-2223−2323−23000000000000002i3−2i32i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000000000
χ7544-4-400-20000−4i4i2-22−2323−232300000000000000−2i32i32i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000000000
χ7644-4-400-20000−4i4i2-22−2323−232300000000000000−2i32i32i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000000000
χ774-44-44-4-24-4-4400-222-2-222000-22−2i22i2−2i22i2−2i22i2−2i22i220000-2000000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ784-44-44-4-24-4-4400-222-2-222000-222i2−2i22i2−2i22i2−2i22i2−2i220000-2000000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ794-44-44-4-2-444-400-22222-2-2000-22−2i22i22i2−2i2−2i22i22i2−2i2-200002000000i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ804-44-44-4-2-444-400-22222-2-2000-222i2−2i2−2i22i22i2−2i2−2i22i2-200002000000−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ814-44-4-44-244-4-400-222-2-2220002-222−2222−22−2222−2222-200002000000−22−222−22−20000000000000000000000000000000000
χ824-44-4-44-244-4-400-222-2-2220002-2−2222−222222−2222−22-2000020000002−22−2−22−220000000000000000000000000000000000
χ834-44-4-44-2-4-44400-22222-2-20002-222−22−2222−222222−2220000-2000000−222−22−2−220000000000000000000000000000000000
χ844-44-4-44-2-4-44400-22222-2-20002-2−222222−2222−22−222220000-20000002−2−22−222−20000000000000000000000000000000000
χ858-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

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