Finite Group Databasebeta

← Group #10691966

Character table — Group #10691966

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222344444466612121212444668888888812121212121288881212242424242424242424242424242424244444444488888888246612124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111-1-111-1-1-1-11111-1-1-1-111-1-1-1iiii−i−i−i−i1111-1-1ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i1-111-1-1i−i1-1
χ101111-1-111-1-1-1-11111-1-1-1-111-1-1-1iiii−i−i−i−i1111-1-1ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−i−i−iiiii1-111-1-1−ii-11
χ111111-1-111-1-1-1-11111-1-1-1-111-1-1-1iiii−i−i−i−i1111-1-1−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i-11-1-111−ii-11
χ121111-1-111-1-1-1-11111-1-1-1-111-1-1-1iiii−i−i−i−i1111-1-1−i−iii1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111−i−i−i−iiiii-11-1-111i−i1-1
χ131111-1-111-1-1-1-11111-1-1-1-111-1-1-1−i−i−i−iiiii1111-1-1ii−i−i1-1iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii-11-1-111i−i-11
χ141111-1-111-1-1-1-11111-1-1-1-111-1-1-1−i−i−i−iiiii1111-1-1ii−i−i1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i-11-1-111−ii1-1
χ151111-1-111-1-1-1-11111-1-1-1-111-1-1-1−i−i−i−iiiii1111-1-1−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii1-111-1-1−ii1-1
χ161111-1-111-1-1-1-11111-1-1-1-111-1-1-1−i−i−i−iiiii1111-1-1−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i1-111-1-1i−i-11
χ172222222222-2-222222222-2-2-22200000000-2-222-2-20000-2-200000000000000002222-2-2-2-2000000000000000000
χ182222222222-2-222222222-2-2-22200000000-2-222-2-20000-2-20000000000000000-2-2-2-22222000000000000000000
χ192222222-2-2-222-2222-2-2-2-22-2-22200000000-2-2-2-22200002-200000000000000000000000022-2-222-2-20000000000
χ202222222-2-2-222-2222-2-2-2-22-2-22200000000-2-2-2-22200002-2000000000000000000000000-2-222-2-2220000000000
χ212222222-2-2-2-2-2-2222-2-2-2-2-222222i2i−2i−2i2i2i−2i−2i22-2-2-2-20000-22000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-2-22222−2i−2i2i2i−2i−2i2i2i22-2-2-2-20000-2200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000
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
χ24222222-1222222-1-1-1-1-1-1-1222-1-122222222-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
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
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i2i2i−2i−2i-1-1111100001-133−3−333−3−3−i−iii−i−iii000000000000000000−i3i3−i3i30000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-12i2i−2i−2i2i2i−2i−2i-1-1111100001-1−3−333−3−333−i−iii−i−iii000000000000000000i3−i3i3−i30000
χ29222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i−2i−2i2i2i-1-1111100001-133−3−333−3−3ii−i−iii−i−i000000000000000000i3−i3i3−i30000
χ30222222-1-2-2-2-2-2-2-1-1-11111-222-1-1−2i−2i2i2i−2i−2i2i2i-1-1111100001-1−3−333−3−333ii−i−iii−i−i000000000000000000−i3i3−i3i30000
χ312222-2-222-2-2222222-2-2-2-2-2-22-2-200000000-2-222220000-22000000000000000022-2-2-2-222000000000000000000
χ322222-2-222-2-2222222-2-2-2-2-2-22-2-200000000-2-222220000-220000000000000000-2-22222-2-2000000000000000000
χ332222-2-22-22222-22222222-22-2-2-222-2-2-2-22222-2-2220000-2-20000000022-2-2-2-22200000000000000000000000000
χ342222-2-22-22222-22222222-22-2-2-2-2-22222-2-222-2-2220000-2-200000000-2-22222-2-200000000000000000000000000
χ352222-2-22-222-2-2-222222222-22-2-200000000-2-2-2-2-2-20000220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ362222-2-22-222-2-2-222222222-22-2-200000000-2-2-2-2-2-2000022000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ372222-2-2-12-2-2-2-22-1-1-1111122-2112i2i2i2i−2i−2i−2i−2i-1-1-1-1112i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii00000000000000002-2-1-1110000
χ382222-2-2-12-2-2-2-22-1-1-1111122-2112i2i2i2i−2i−2i−2i−2i-1-1-1-111−2i−2i2i2i-11iiii−i−i−i−i−i−i−i−iiiii0000000000000000-2211-1-10000
χ392222-2-2-12-2-2-2-22-1-1-1111122-211−2i−2i−2i−2i2i2i2i2i-1-1-1-1112i2i−2i−2i-11−i−i−i−iiiiiiiii−i−i−i−i0000000000000000-2211-1-10000
χ402222-2-2-12-2-2-2-22-1-1-1111122-211−2i−2i−2i−2i2i2i2i2i-1-1-1-111−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i00000000000000002-2-1-1110000
χ412222-2-2-1-22222-2-1-1-1-1-1-1-1-22-21122-2-2-2-222-1-111-1-1000011−i3−i3i3i3i3i3−i3−i3-1-11111-1-1000000000000000000−i3i3i3−i30000
χ422222-2-2-1-22222-2-1-1-1-1-1-1-1-22-21122-2-2-2-222-1-111-1-1000011i3i3−i3−i3−i3−i3i3i3-1-11111-1-1000000000000000000i3−i3−i3i30000
χ432222-2-2-1-22222-2-1-1-1-1-1-1-1-22-211-2-22222-2-2-1-111-1-1000011−i3−i3i3i3i3i3−i3−i311-1-1-1-111000000000000000000i3−i3−i3i30000
χ442222-2-2-1-22222-2-1-1-1-1-1-1-1-22-211-2-22222-2-2-1-111-1-1000011i3i3−i3−i3−i3−i3i3i311-1-1-1-111000000000000000000−i3i3i3−i30000
χ452-2-222-222-2200-2-2-22-2-2220002-22−22−22−22−2002-200000000000000002−22−22−22−22i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000000000
χ462-2-222-222-2200-2-2-22-2-2220002-22−22−22−22−2002-200000000000000002−22−22−22−2−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000000000
χ472-2-222-222-2200-2-2-22-2-2220002-2−22−22−22−22002-20000000000000000−22−22−22−222i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i20000000000
χ482-2-222-222-2200-2-2-22-2-2220002-2−22−22−22−22002-20000000000000000−22−22−22−22−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i20000000000
χ492-2-222-22-22-2002-2-2222-2-20002-2−i2i2i2−i2−i2i2i2−i200-220000000000000000−i2i2i2−i2−i2i2i2−i200002-22-2−i2i2i2−i2−i2i2i2−i20000000000
χ502-2-222-22-22-2002-2-2222-2-20002-2−i2i2i2−i2−i2i2i2−i200-220000000000000000−i2i2i2−i2−i2i2i2−i20000-22-22i2−i2−i2i2i2−i2−i2i20000000000
χ512-2-222-22-22-2002-2-2222-2-20002-2i2−i2−i2i2i2−i2−i2i200-220000000000000000i2−i2−i2i2i2−i2−i2i200002-22-2i2−i2−i2i2i2−i2−i2i20000000000
χ522-2-222-22-22-2002-2-2222-2-20002-2i2−i2−i2i2i2−i2−i2i200-220000000000000000i2−i2−i2i2i2−i2−i2i20000-22-22−i2i2i2−i2−i2i2i2−i20000000000
χ532-2-22-22222-200-2-2-2222-2-2000-22−i2i2−i2i2i2−i2i2−i2002-20000000000000000−i2i2−i2i2i2−i2i2−i22i−2i−2i2i0000−22−222−22−20000000000
χ542-2-22-22222-200-2-2-2222-2-2000-22−i2i2−i2i2i2−i2i2−i2002-20000000000000000−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i00002−22−2−22−220000000000
χ552-2-22-22222-200-2-2-2222-2-2000-22i2−i2i2−i2−i2i2−i2i2002-20000000000000000i2−i2i2−i2−i2i2−i2i22i−2i−2i2i00002−22−2−22−220000000000
χ562-2-22-22222-200-2-2-2222-2-2000-22i2−i2i2−i2−i2i2−i2i2002-20000000000000000i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i0000−22−222−22−20000000000
χ572-2-22-222-2-22002-2-22-2-222000-222−2−22−222−200-2200000000000000002−2−22−222−200002-2-222−2−22−222−20000000000
χ582-2-22-222-2-22002-2-22-2-222000-222−2−22−222−200-2200000000000000002−2−22−222−20000-222-2−222−22−2−220000000000
χ592-2-22-222-2-22002-2-22-2-222000-22−222−22−2−2200-220000000000000000−222−22−2−2200002-2-22−222−22−2−220000000000
χ602-2-22-222-2-22002-2-22-2-222000-22−222−22−2−2200-220000000000000000−222−22−2−220000-222-22−2−22−222−20000000000
χ61444444-2444-4-44-2-2-2-2-2-2-2-4-4-4-2-20000000022-2-222000022000000000000000000000000000000000000000000
χ62444444-2-4-4-444-4-2-2-222224-4-4-2-2000000002222-2-20000-22000000000000000000000000000000000000000000
χ634444-4-4-24-4-4444-2-2-22222-4-44220000000022-2-2-2-200002-2000000000000000000000000000000000000000000
χ644444-4-4-2-444-4-4-4-2-2-2-2-2-2-24-4422000000002222220000-2-2000000000000000000000000000000000000000000
χ654-44-40040004i−4i04-4-40000000000000000000004i−4i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000
χ664-44-40040004i−4i04-4-40000000000000000000004i−4i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000
χ674-44-4004000−4i4i04-4-4000000000000000000000−4i4i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000
χ684-44-4004000−4i4i04-4-4000000000000000000000−4i4i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000
χ694-44-400-20004i−4i0-22223−2323−230000000000000−2i32i300−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ72ζ7−2ζ232ζ232ζ5−2ζ52ζ13−2ζ130000000000000000000000000000000000
χ704-44-400-20004i−4i0-22223−2323−230000000000000−2i32i300−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ7−2ζ72ζ23−2ζ23−2ζ52ζ5−2ζ132ζ130000000000000000000000000000000000
χ714-44-400-20004i−4i0-222−2323−232300000000000002i3−2i300−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ232ζ23−2ζ72ζ72ζ13−2ζ132ζ5−2ζ50000000000000000000000000000000000
χ724-44-400-20004i−4i0-222−2323−232300000000000002i3−2i300−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ23−2ζ232ζ7−2ζ7−2ζ132ζ13−2ζ52ζ50000000000000000000000000000000000
χ734-44-400-2000−4i4i0-22223−2323−2300000000000002i3−2i3002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ5−2ζ52ζ13−2ζ13−2ζ72ζ7−2ζ232ζ230000000000000000000000000000000000
χ744-44-400-2000−4i4i0-22223−2323−2300000000000002i3−2i3002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ52ζ5−2ζ132ζ132ζ7−2ζ72ζ23−2ζ230000000000000000000000000000000000
χ754-44-400-2000−4i4i0-222−2323−23230000000000000−2i32i3002i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ13−2ζ132ζ5−2ζ5−2ζ232ζ23−2ζ72ζ70000000000000000000000000000000000
χ764-44-400-2000−4i4i0-222−2323−23230000000000000−2i32i3002i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ132ζ13−2ζ52ζ52ζ23−2ζ232ζ7−2ζ70000000000000000000000000000000000
χ774-4-444-4-24-4400-422-222-2-2000-2222−2222−2222−2222−2200-220000000000000000−22−22−22−2200000000000000000000000000
χ784-4-444-4-24-4400-422-222-2-2000-22−2222−2222−2222−222200-2200000000000000002−22−22−22−200000000000000000000000000
χ794-4-444-4-2-44-400422-2-2-222000-22−2i22i22i2−2i2−2i22i22i2−2i2002-20000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ804-4-444-4-2-44-400422-2-2-222000-222i2−2i2−2i22i22i2−2i2−2i22i2002-20000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ814-4-44-44-244-400-422-2-2-2220002-2−2i22i2−2i22i22i2−2i22i2−2i200-220000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ824-4-44-44-244-400-422-2-2-2220002-22i2−2i22i2−2i2−2i22i2−2i22i200-220000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ834-4-44-44-2-4-4400422-222-2-20002-222−22−2222−222222−22002-20000000000000000−222−22−2−2200000000000000000000000000
χ844-4-44-44-2-4-4400422-222-2-20002-2−222222−2222−22−2222002-200000000000000002−2−22−222−200000000000000000000000000
χ8588-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000000

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