Finite Group Databasebeta

← Group #10696519

Character table — Group #10696519

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222444444444444448888888888888888888888888816161616161624242424484848484848
order122222223666666644444412121212121212128888888812122424242424242424242424242424242444121212128888244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-111-1-1-1
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ922222222222222222-2-2-2-22-2-2-2-2-2-2-2-2000000002200000000000000002-222-2-20000000000
χ1022222222222222222-2-2-2-22-2-2-2-2-2-2-2-200000000220000000000000000-22-2-2220000000000
χ112222222222222222-22-22-2-222-2-222-2-200000000-2-200000000000000000000000000200-200
χ122222222222222222-22-22-2-222-2-222-2-200000000-2-200000000000000000000000000-200200
χ132222222222222222-2-22-22-2-2-222-2-22200000000-2-20000000000000000000000000002-2000
χ142222222222222222-2-22-22-2-2-222-2-22200000000-2-2000000000000000000000000000-22000
χ1522222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ1622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ1722222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ1822222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000
χ1922222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-13333−3−3−3−33333−3−3−3−32-2-1-1110000000000
χ2022222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-13333−3−3−3−3−3−3−3−33333-2211-1-10000000000
χ2122222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-1−3−3−3−333333333−3−3−3−3-2211-1-10000000000
χ2222222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-1−3−3−3−33333−3−3−3−333332-2-1-1110000000000
χ232-2-22-2-2222-2-2-2-2222222-2-2-22222-2-2-2-22i2i−2i−2i00002-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ242-2-22-2-2222-2-2-2-2222222-2-2-22222-2-2-2-2−2i−2i2i2i00002-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ252-2-22-2-2222-2-2-2-22222-2-222-2-2-2-2-22222000022-2-22-20000000022-2-222-2-20000000000000000
χ262-2-22-2-2222-2-2-2-22222-2-222-2-2-2-2-222220000-2-2222-200000000-2-222-2-2220000000000000000
χ272-2-22-2-2222-2-2-2-2222-22-2-22222-2-2-2-22200000000-22000000000000000000000022-2-2000000
χ282-2-22-2-2222-2-2-2-2222-22-2-22222-2-2-2-22200000000-220000000000000000000000-2-222000000
χ292-2-22-2-2222-2-2-2-2222-2-222-22-2-22222-2-200000000-220000000000000000000000000000002-2
χ302-2-22-2-2222-2-2-2-2222-2-222-22-2-22222-2-200000000-22000000000000000000000000000000-22
χ312-2-22-2-222-11111-1-1-1222-2-2-2-1-1-1-111112i2i−2i−2i0000-11−i−iii−i−iii33−3−3−3−33300−i3i3−i3i30000000000
χ322-2-22-2-222-11111-1-1-1222-2-2-2-1-1-1-111112i2i−2i−2i0000-11−i−iii−i−iii−3−33333−3−300i3−i3i3−i30000000000
χ332-2-22-2-222-11111-1-1-1222-2-2-2-1-1-1-11111−2i−2i2i2i0000-11ii−i−iii−i−i33−3−3−3−33300i3−i3i3−i30000000000
χ342-2-22-2-222-11111-1-1-1222-2-2-2-1-1-1-11111−2i−2i2i2i0000-11ii−i−iii−i−i−3−33333−3−300−i3i3−i3i30000000000
χ352-2-22-2-222-11111-1-1-12-2-222-21111-1-1-1-1000022-2-2-11−i3−i3i3i3i3i3−i3−i3-1-111-1-11100−i3i3i3−i30000000000
χ362-2-22-2-222-11111-1-1-12-2-222-21111-1-1-1-1000022-2-2-11i3i3−i3−i3−i3−i3i3i3-1-111-1-11100i3−i3−i3i30000000000
χ372-2-22-2-222-11111-1-1-12-2-222-21111-1-1-1-10000-2-222-11−i3−i3i3i3i3i3−i3−i311-1-111-1-100i3−i3−i3i30000000000
χ382-2-22-2-222-11111-1-1-12-2-222-21111-1-1-1-10000-2-222-11i3i3−i3−i3−i3−i3i3i311-1-111-1-100−i3i3i3−i30000000000
χ3944444444-2-2-2-2-2-2-2-2-44-44-4-4-2-222-2-222000000002200000000000000000000000000000000
χ4044444444-2-2-2-2-2-2-2-2-4-44-44-422-2-222-2-2000000002200000000000000000000000000000000
χ41444-4-4-4-44444-4-4-44-4000000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ42444-4-4-4-44444-4-4-44-400000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ43444-4-4-4-44-2-2-2222-2200000023−230023−23002i−2i2i−2i000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ44444-4-4-4-44-2-2-2222-2200000023−230023−2300−2i2i−2i2i000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ45444-4-4-4-44-2-2-2222-22000000−232300−2323002i−2i2i−2i000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ46444-4-4-4-44-2-2-2222-22000000−232300−232300−2i2i−2i2i000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ4744-444-4-4-444-44-44-4-400000000000000000000000000000000000000000000002-22-2000000
χ4844-444-4-4-444-44-44-4-40000000000000000000000000000000000000000000000-22-22000000
χ4944-4-4-444-444-4-44-4-440000000000000000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ5044-4-4-444-444-4-44-4-44000000000000000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ5144-4-4-444-4-2-222-222-20000000023−230023−2300002i−2i2i−2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000
χ5244-4-4-444-4-2-222-222-20000000023−230023−230000−2i2i−2i2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000
χ5344-4-4-444-4-2-222-222-200000000−232300−232300002i−2i2i−2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000
χ5444-4-4-444-4-2-222-222-200000000−232300−23230000−2i2i−2i2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000
χ554-444-44-4-44-44-444-4-400000000000000000000000000000000000000000000002-2-22000000
χ564-444-44-4-44-44-444-4-40000000000000000000000000000000000000000000000-222-2000000
χ574-44-44-44-44-444-4-4-440000000000000000002i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ584-44-44-44-44-444-4-4-44000000000000000000−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ594-44-44-44-4-22-2-2222-20000000023−2300−232300002i−2i−2i2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000
χ604-44-44-44-4-22-2-2222-20000000023−2300−23230000−2i2i2i−2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000
χ614-44-44-44-4-22-2-2222-200000000−23230023−2300002i−2i−2i2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000
χ624-44-44-44-4-22-2-2222-200000000−23230023−230000−2i2i2i−2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000
χ634-4-44-4-444-22222-2-2-2-44-4-444-2-22222-2-2000000002-200000000000000000000000000000000
χ644-4-44-4-444-22222-2-2-2-4-444-4422-2-2-2-222000000002-200000000000000000000000000000000
χ654-4-4-444-444-4-444-44-4000000000000002-2-220000002-2-222-2-22000000000000000000000000
χ664-4-4-444-444-4-444-44-400000000000000-222-2000000-222-2-222-2000000000000000000000000
χ674-4-4-444-44-222-2-22-2200000023−2300−2323002-2-22000000−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000
χ684-4-4-444-44-222-2-22-2200000023−2300−232300-222-20000001+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000
χ694-4-4-444-44-222-2-22-22000000−23230023−23002-2-22000000−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000
χ704-4-4-444-44-222-2-22-22000000−23230023−2300-222-20000001−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000
χ7188-888-8-8-8-4-44-44-44400000000000000000000000000000000000000000000000000000000
χ728-888-88-8-8-44-44-4-44400000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.