Finite Group Databasebeta

← Group #10690086

Character table — Group #10690086

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222244444444444444888888888888888888888888888888161616162424242424242424242424244848
order1222444436661212121224444466121212121212244444448888121212121212121212122424242424242424612121288888888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−iii−i−i11-1-11-1
χ101111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1−ii−ii−i−iii-1-111-11
χ111111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1i−ii−iii−i−i-1-111-11
χ121111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii−i−iii11-1-11-1
χ131111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-1-1-111ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii-1-111i−ii−i−i−iii11-1-1-11
χ141111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-1-1-111ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii-1-111−ii−iiii−i−i-1-1111-1
χ151111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-1-1-111−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111i−ii−i−i−iii-1-1111-1
χ161111-1-1-1-11111-1-1-1-1-11-11-11-1-11111-1-1-1-111−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−ii−iiii−i−i11-1-1-11
χ1722222222222222222-2-22-2-22222-2-2-2-2000000000000-2-20000000000000000000000002-22-2000000
χ1822222222222222222-2-22-2-22222-2-2-2-2000000000000-2-2000000000000000000000000-22-22000000
χ192222222222222222-22-2-22-2-2-2-2-22222000000000000-2-20000000000000000000022-2-20000000000
χ202222222222222222-22-2-22-2-2-2-2-22222000000000000-2-200000000000000000000-2-2220000000000
χ212222222222222222-2-22-2-22-2-2-2-2-2-2-2-22-2-22000000002200000000000000002-22-200000000000000
χ222222222222222222-2-22-2-22-2-2-2-2-2-2-2-2-222-200000000220000000000000000-22-2200000000000000
χ2322222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2422222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-11111111111111111-1-1-1-100000000000000
χ2522222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000000000
χ2622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1111100000000000000
χ2722222222-1-1-1-1-1-1-1-1-2-22-2-22111111112-2-2200000000-1-133−3−333−3−333−3−333−3−3-11-1100000000000000
χ2822222222-1-1-1-1-1-1-1-1-2-22-2-22111111112-2-2200000000-1-1−3−333−3−333−3−333−3−333-11-1100000000000000
χ2922222222-1-1-1-1-1-1-1-1-2-22-2-2211111111-222-200000000-1-133−3−333−3−3−3−333−3−3331-11-100000000000000
χ3022222222-1-1-1-1-1-1-1-1-2-22-2-2211111111-222-200000000-1-1−3−333−3−33333−3−333−3−31-11-100000000000000
χ312222-2-2-2-22222-2-2-2-2222-2-2-222-2-222-2-2000000000000-22000000000000000000002i−2i−2i2i0000000000
χ322222-2-2-2-22222-2-2-2-2222-2-2-222-2-222-2-2000000000000-2200000000000000000000−2i2i2i−2i0000000000
χ332222-2-2-2-22222-2-2-2-22-2-2-22222-2-2-2-2222-22-2000000002-200000000000000002-2-2200000000000000
χ342222-2-2-2-22222-2-2-2-22-2-2-22222-2-2-2-222-22-22000000002-20000000000000000-222-200000000000000
χ352222-2-2-2-22222-2-2-2-2-2-2222-2-2-222-2-222000000000000-220000000000000000000000002i−2i−2i2i000000
χ362222-2-2-2-22222-2-2-2-2-2-2222-2-2-222-2-222000000000000-22000000000000000000000000−2i2i2i−2i000000
χ372222-2-2-2-2-1-1-1-111112-2-2-222-1-11111-1-12-22-200000000-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-111-100000000000000
χ382222-2-2-2-2-1-1-1-111112-2-2-222-1-11111-1-12-22-200000000-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-111-100000000000000
χ392222-2-2-2-2-1-1-1-111112-2-2-222-1-11111-1-1-22-2200000000-11−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31-1-1100000000000000
χ402222-2-2-2-2-1-1-1-111112-2-2-222-1-11111-1-1-22-2200000000-11i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31-1-1100000000000000
χ412222-2-2-2-2-1-1-1-11111-22-22-2211-1-1-1-11122-2-22i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii-1-11100000000000000
χ422222-2-2-2-2-1-1-1-11111-22-22-2211-1-1-1-11122-2-2−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i-1-11100000000000000
χ432222-2-2-2-2-1-1-1-11111-22-22-2211-1-1-1-111-2-2222i2i−2i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i11-1-100000000000000
χ442222-2-2-2-2-1-1-1-11111-22-22-2211-1-1-1-111-2-222−2i−2i2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii11-1-100000000000000
χ4544444444-2-2-2-2-2-2-2-24-4-44-4-4-2-2-2-22222000000000000220000000000000000000000000000000000
χ4644444444-2-2-2-2-2-2-2-2-44-4-44-42222-2-2-2-2000000000000220000000000000000000000000000000000
χ474444-4-4-4-4-2-2-2-22222444-4-4-4-2-222-2-2220000000000002-20000000000000000000000000000000000
χ484444-4-4-4-4-2-2-2-22222-4-4444-422-2-222-2-20000000000002-20000000000000000000000000000000000
χ4944-4-44i−4i4i−4i44-4-44i4i−4i−4i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ5044-4-44i−4i4i−4i44-4-44i4i−4i−4i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ5144-4-44i−4i4i−4i-2-222−2i−2i2i2i000000−2i32i323−230000000000002ζ7+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+ζ23000000000000000000
χ5244-4-44i−4i4i−4i-2-222−2i−2i2i2i000000−2i32i323−23000000000000−2ζ7−2ζ232ζ7+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−ζ23000000000000000000
χ5344-4-44i−4i4i−4i-2-222−2i−2i2i2i0000002i3−2i3−23230000000000002ζ7+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−ζ23000000000000000000
χ5444-4-44i−4i4i−4i-2-222−2i−2i2i2i0000002i3−2i3−2323000000000000−2ζ7−2ζ232ζ7+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+ζ23000000000000000000
χ5544-4-4−4i4i−4i4i44-4-4−4i−4i4i4i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ5644-4-4−4i4i−4i4i44-4-4−4i−4i4i4i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ5744-4-4−4i4i−4i4i-2-2222i2i−2i−2i000000−2i32i3−2323000000000000−2ζ5−2ζ132ζ5+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+ζ23000000000000000000
χ5844-4-4−4i4i−4i4i-2-2222i2i−2i−2i000000−2i32i3−23230000000000002ζ5+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−ζ23000000000000000000
χ5944-4-4−4i4i−4i4i-2-2222i2i−2i−2i0000002i3−2i323−23000000000000−2ζ5−2ζ132ζ5+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+ζ23000000000000000000
χ6044-4-4−4i4i−4i4i-2-2222i2i−2i−2i0000002i3−2i323−230000000000002ζ5+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−ζ23000000000000000000
χ614-44-44i−4i−4i4i4-44-44i−4i4i−4i000000000000000000000000000000000000000000000000000000002-22i−2i00
χ624-44-44i−4i−4i4i4-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000000000-22−2i2i00
χ634-44-4−4i4i4i−4i4-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000000000002-2−2i2i00
χ644-44-4−4i4i4i−4i4-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000000000-222i−2i00
χ654-4-4444-4-44-4-444-4-440000000000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ664-4-4444-4-44-4-444-4-44000000000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ674-4-4444-4-4-222-2-222-2000000000023−2323−2300002i−2i2i−2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000000000000000
χ684-4-4444-4-4-222-2-222-2000000000023−2323−230000−2i2i−2i2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000000000000000
χ694-4-4444-4-4-222-2-222-20000000000−2323−232300002i−2i2i−2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000000000000000
χ704-4-4444-4-4-222-2-222-20000000000−2323−23230000−2i2i−2i2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000000000000000
χ714-4-44-4-4444-4-44-444-40000000000000000002-2-220000002-22-2-22-2200000000000000000000000000
χ724-4-44-4-4444-4-44-444-4000000000000000000-222-2000000-22-222-22-200000000000000000000000000
χ734-4-44-4-444-222-22-2-22000000000023−23−232300002-2-22000000−1−31+3−1+31−31+3−1−31−3−1+300000000000000000000000000
χ744-4-44-4-444-222-22-2-22000000000023−23−23230000-222-20000001+3−1−31−3−1+3−1−31+3−1+31−300000000000000000000000000
χ754-4-44-4-444-222-22-2-220000000000−232323−2300002-2-22000000−1+31−3−1−31+31−3−1+31+3−1−300000000000000000000000000
χ764-4-44-4-444-222-22-2-220000000000−232323−230000-222-20000001−3−1+31+3−1−3−1+31−3−1−31+300000000000000000000000000
χ778-88-88i−8i−8i8i-44-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ788-88-8−8i8i8i−8i-44-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000

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