Finite Group Databasebeta

← Group #10698926

Character table — Group #10698926

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222344444466612121212444661212121212128888888812122424242424242424242424242424242424661212224488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ9222222222-2-2222222222-2-2-222-2-22-2-2200000000-2-2000000000000000000000022-2-200000000
χ10222222222-2-2222222222-2-2-222-2-22-2-2200000000-2-20000000000000000000000-2-22200000000
χ112222222-2-222-2-2222-2-2-2-22-2-22222-2-2-2-200002i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i00000000000000000000000000
χ122222222-2-222-2-2222-2-2-2-22-2-22222-2-2-2-20000−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000000000
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-222-200000000-220000000000000000000000000022-2-20000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-222-200000000-2200000000000000000000000000-2-2220000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ19222222-1-2-222-2-2-1-1-111112-2-2-1-1-1-1111100002i2i−2i−2i-11−i−i−i−iiiii3333−3−3−3−300−i3i3−i3i3000000000000
χ20222222-1-2-222-2-2-1-1-111112-2-2-1-1-1-1111100002i2i−2i−2i-11−i−i−i−iiiii−3−3−3−3333300i3−i3i3−i3000000000000
χ21222222-1-2-222-2-2-1-1-111112-2-2-1-1-1-111110000−2i−2i2i2i-11iiii−i−i−i−i3333−3−3−3−300i3−i3i3−i3000000000000
χ22222222-1-2-222-2-2-1-1-111112-2-2-1-1-1-111110000−2i−2i2i2i-11iiii−i−i−i−i−3−3−3−3333300−i3i3−i3i3000000000000
χ232222-2-222222-2-22222222-22-2-2-222-222-200000000-2-20000000000000000000000000000002i−2i00
χ242222-2-222222-2-22222222-22-2-2-222-222-200000000-2-2000000000000000000000000000000−2i2i00
χ252222-2-2222-2-2-2-222222222-22-2-2-2-2-2-2-2-22i2i−2i−2i000022000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ262222-2-2222-2-2-2-222222222-22-2-2-2-2-2-2-2-2−2i−2i2i2i00002200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ272222-2-22-2-22222222-2-2-2-2-2-22-2-2222-2-2200000000-22000000000000000000000000000000002-2
χ282222-2-22-2-22222222-2-2-2-2-2-22-2-2222-2-2200000000-2200000000000000000000000000000000-22
χ292222-2-22-2-2-2-222222-2-2-2-222-2-2-2-2-22222000000002-200000000000000002-222-2-2000000000000
χ302222-2-22-2-2-2-222222-2-2-2-222-2-2-2-2-22222000000002-20000000000000000-22-2-222000000000000
χ312222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-22111111112i2i−2i−2i0000-1-133−3−333−3−3−i−iii−i−iii00−i3i3i3−i3000000000000
χ322222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-22111111112i2i−2i−2i0000-1-1−3−333−3−333−i−iii−i−iii00i3−i3−i3i3000000000000
χ332222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-2211111111−2i−2i2i2i0000-1-133−3−333−3−3ii−i−iii−i−i00i3−i3−i3i3000000000000
χ342222-2-2-122-2-2-2-2-1-1-1-1-1-1-12-2211111111−2i−2i2i2i0000-1-1−3−333−3−333ii−i−iii−i−i00−i3i3i3−i3000000000000
χ352222-2-2-1-2-2-2-222-1-1-1111122-21111-1-1-1-100000000-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-1-111000000000000
χ362222-2-2-1-2-2-2-222-1-1-1111122-21111-1-1-1-100000000-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-2211-1-1000000000000
χ372222-2-2-1-2-2-2-222-1-1-1111122-21111-1-1-1-100000000-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-2211-1-1000000000000
χ382222-2-2-1-2-2-2-222-1-1-1111122-21111-1-1-1-100000000-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-1-111000000000000
χ392-22-22-222-2002-2-2-2222-2-20002-200-200200002−22−2002−22−22−22−200000000000000002i−2i−i2i2−i2i20000
χ402-22-22-222-2002-2-2-2222-2-20002-200-200200002−22−2002−22−22−22−20000000000000000−2i2ii2−i2i2−i20000
χ412-22-22-222-2002-2-2-2222-2-20002-200-20020000−22−2200−22−22−22−2200000000000000002i−2ii2−i2i2−i20000
χ422-22-22-222-2002-2-2-2222-2-20002-200-20020000−22−2200−22−22−22−220000000000000000−2i2i−i2i2−i2i20000
χ432-22-22-22-2200-22-2-22-2-2220002-200200-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000002-200−i2i2i2−i20000
χ442-22-22-22-2200-22-2-22-2-2220002-200200-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000000000-2200i2−i2−i2i20000
χ452-22-22-22-2200-22-2-22-2-2220002-200200-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000002-200i2−i2−i2i20000
χ462-22-22-22-2200-22-2-22-2-2220002-200200-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000000000-2200−i2i2i2−i20000
χ47444444-244-4-444-2-2-2-2-2-2-2-4-4-4-2-222-222-200000000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-22222-444-2-2222-2-22000000002-20000000000000000000000000000000000
χ494444-4-4-24444-4-4-2-2-2-2-2-2-2-44-422-2-22-2-2200000000220000000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-22222-4-4422-2-2-222-2000000002-20000000000000000000000000000000000
χ5144-4-4004004i−4i004-4-40000000004i−4i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ5244-4-4004004i−4i004-4-40000000004i−4i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ5344-4-400400−4i4i004-4-4000000000−4i4i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ5444-4-400400−4i4i004-4-4000000000−4i4i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ5544-4-400-2004i−4i00-22223−2323−2300000−2i2i0−2i32i302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000ζ5−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+ζ23000000000000000000
χ5644-4-400-2004i−4i00-22223−2323−2300000−2i2i0−2i32i30−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−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−ζ23000000000000000000
χ5744-4-400-2004i−4i00-222−2323−232300000−2i2i02i3−2i302ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−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−ζ23000000000000000000
χ5844-4-400-2004i−4i00-222−2323−232300000−2i2i02i3−2i30−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000ζ5+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+ζ23000000000000000000
χ5944-4-400-200−4i4i00-22223−2323−23000002i−2i02i3−2i30−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5−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+ζ23000000000000000000
χ6044-4-400-200−4i4i00-22223−2323−23000002i−2i02i3−2i302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−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−ζ23000000000000000000
χ6144-4-400-200−4i4i00-222−2323−2323000002i−2i0−2i32i30−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5+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+ζ23000000000000000000
χ6244-4-400-200−4i4i00-222−2323−2323000002i−2i0−2i32i302ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−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−ζ23000000000000000000
χ634-44-44-4-24-4004-422-2-2-222000-2200200-2000022−2222−2200−22−22−22−2200000000000000000000000000
χ644-44-44-4-24-4004-422-2-2-222000-2200200-20000−2222−2222002−22−22−22−200000000000000000000000000
χ654-44-44-4-2-4400-4422-222-2-2000-2200-20020000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ664-44-44-4-2-4400-4422-222-2-2000-2200-200200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ674-44-4-4444-400-44-4-4444-4-4000-4400400-400000000000000000000000000000000000000000000
χ684-44-4-444-44004-4-4-44-4-444000-4400-400400000000000000000000000000000000000000000000
χ694-44-4-44-24-400-4422-2-2-2220002-200-200200000000006−6−666−6−6600000000000000000000000000
χ704-44-4-44-24-400-4422-2-2-2220002-200-20020000000000−666−6−666−600000000000000000000000000
χ714-44-4-44-2-44004-422-222-2-20002-200200-20000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ724-44-4-44-2-44004-422-222-2-20002-200200-20000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ738-8-88008000000-88-800000000000000000000000000000000000000000000000000000000000
χ748-8-8800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000
χ758-8-8800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000

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