Finite Group Databasebeta

← Group #10690101

Character table — Group #10690101

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222244444444444444888888888888888888888888888888161616162424242424242424242424244848
order122222223666666644444412121212121212124444888888881212242424242424242424242424242424241212121222444444888844
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
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1
χ91-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1i−ii−iii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−i1-1i−i1-1i−iii−i−i1-1
χ101-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1i−ii−iii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−i-11−ii-11−ii−i−iii-11
χ111-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1i−ii−i−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111ii−i−i1-1i−i1-1i−i−i−iii-11
χ121-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1i−ii−i−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111ii−i−i-11−ii-11−iiii−i−i1-1
χ131-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1−ii−iiii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−iii1-1−ii1-1−iiii−i−i-11
χ141-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1−ii−iiii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−iii-11i−i-11i−i−i−iii1-1
χ151-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1−ii−ii−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iii1-1−ii1-1−ii−i−iii1-1
χ161-11-1-11-111-1-1111-1-11-111-1-111-1-111-1-1−ii−ii−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iii-11i−i-11i−iii−i−i-11
χ1722222222222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-2000000002200000000000000002-22-200000000000000
χ1822222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-22200000000220000000000000000-22-2200000000000000
χ192222222222222222-22-22-2-2-2-22222-2-2000000000000-2-2000000000000000000002200-2-200000000
χ202222222222222222-22-22-2-2-2-22222-2-2000000000000-2-200000000000000000000-2-2002200000000
χ212222222222222222-2-22-22-222-2-2-2-222000000000000-2-200000000000000000000002200-2-2000000
χ222222222222222222-2-22-22-222-2-2-2-222000000000000-2-20000000000000000000000-2-20022000000
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
χ2722222222-1-1-1-1-1-1-1-12-2-2-2-221111111122-2-200000000-1-133−3−333−3−333−3−333−3−3-11-1100000000000000
χ2822222222-1-1-1-1-1-1-1-12-2-2-2-221111111122-2-200000000-1-1−3−333−3−333−3−333−3−333-11-1100000000000000
χ2922222222-1-1-1-1-1-1-1-12-2-2-2-2211111111-2-22200000000-1-133−3−333−3−3−3−333−3−3331-11-100000000000000
χ3022222222-1-1-1-1-1-1-1-12-2-2-2-2211111111-2-22200000000-1-1−3−333−3−33333−3−333−3−31-11-100000000000000
χ312-22-2-22-222-2-2222-2-222-2-22-2-2-222-2-2222i−2i−2i2i000000002-200000000000000002i−2i−2i2i00000000000000
χ322-22-2-22-222-2-2222-2-222-2-22-2-2-222-2-222−2i2i2i−2i000000002-20000000000000000−2i2i2i−2i00000000000000
χ332-22-2-22-222-2-2222-2-2-222-2-222222-2-2-2-2000000000000-2200000000000000000000002i−2i00−2i2i000000
χ342-22-2-22-222-2-2222-2-2-222-2-222222-2-2-2-2000000000000-220000000000000000000000−2i2i002i−2i000000
χ352-22-2-22-222-2-2222-2-2-2-2-2222-2-2-2-22222000000000000-22000000000000000000002-200-2200000000
χ362-22-2-22-222-2-2222-2-2-2-2-2222-2-2-2-22222000000000000-2200000000000000000000-22002-200000000
χ372-22-2-22-22-111-1-1-11122-2-22-211-1-111-1-12i−2i−2i2i00000000-11−i3−i3i3i3i3i3−i3−i3−3−33333−3−3−iii−i00000000000000
χ382-22-2-22-22-111-1-1-11122-2-22-211-1-111-1-12i−2i−2i2i00000000-11i3i3−i3−i3−i3−i3i3i333−3−3−3−333−iii−i00000000000000
χ392-22-2-22-22-111-1-1-11122-2-22-211-1-111-1-1−2i2i2i−2i00000000-11−i3−i3i3i3i3i3−i3−i333−3−3−3−333i−i−ii00000000000000
χ402-22-2-22-22-111-1-1-11122-2-22-211-1-111-1-1−2i2i2i−2i00000000-11i3i3−i3−i3−i3−i3i3i3−3−33333−3−3i−i−ii00000000000000
χ412-22-2-22-22-111-1-1-1112-222-2-2-1-111-1-1112i−2i2i−2i2i2i−2i−2i22-2-2-11−i−i−i−iiiii-1-1-1-11111−i−iii00000000000000
χ422-22-2-22-22-111-1-1-1112-222-2-2-1-111-1-1112i−2i2i−2i−2i−2i2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-1−i−iii00000000000000
χ432-22-2-22-22-111-1-1-1112-222-2-2-1-111-1-111−2i2i−2i2i2i2i−2i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-1ii−i−i00000000000000
χ442-22-2-22-22-111-1-1-1112-222-2-2-1-111-1-111−2i2i−2i2i−2i−2i2i2i22-2-2-11iiii−i−i−i−i-1-1-1-11111ii−i−i00000000000000
χ4544444444-2-2-2-2-2-2-2-2-44-44-4-422-2-2-2-222000000000000220000000000000000000000000000000000
χ4644444444-2-2-2-2-2-2-2-2-4-44-44-4-2-22222-2-2000000000000220000000000000000000000000000000000
χ47444-44-4-4-44444-4-4-4-4000000000000000000000000000000000000000000000000000000002-22-200
χ48444-44-4-4-44444-4-4-4-400000000000000000000000000000000000000000000000000000000-22-2200
χ4944-44-4-4-4444-4-44-44-40000000000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ5044-44-4-4-4444-4-44-44-4000000000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ5144-44-4-4-44-2-222-22-220000000023−2323−230000002i−2i2i−2i000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ5244-44-4-4-44-2-222-22-220000000023−2323−23000000−2i2i−2i2i000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ5344-44-4-4-44-2-222-22-2200000000−2323−23230000002i−2i2i−2i000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ5444-44-4-4-44-2-222-22-2200000000−2323−2323000000−2i2i−2i2i000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ5544-4-4-444-444-4-4-44-4400000000000000000000002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ5644-4-4-444-444-4-4-44-440000000000000000000000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ5744-4-4-444-4-2-2222-22-200000023−23000023−23000000002i−2i2i−2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000
χ5844-4-4-444-4-2-2222-22-200000023−23000023−2300000000−2i2i−2i2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000
χ5944-4-4-444-4-2-2222-22-2000000−23230000−2323000000002i−2i2i−2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000
χ6044-4-4-444-4-2-2222-22-2000000−23230000−232300000000−2i2i−2i2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000
χ614-444-4-44-44-4-44-4-444000000000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ624-444-4-44-44-4-44-4-44400000000000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ634-44-4-44-44-222-2-2-222-444-4-44-2-2-2-222220000000000002-20000000000000000000000000000000000
χ644-44-4-44-44-222-2-2-222-4-4-44442222-2-2-2-20000000000002-20000000000000000000000000000000000
χ654-4-4444-4-44-44-4-444-400000000000000000000002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ664-4-4444-4-44-44-4-444-40000000000000000000000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ674-4-4444-4-4-22-222-2-2200000023−230000−2323000000002i−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+ζ11000000000000000000
χ684-4-4444-4-4-22-222-2-2200000023−230000−232300000000−2i2i2i−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−ζ11000000000000000000
χ694-4-4444-4-4-22-222-2-22000000−2323000023−23000000002i−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+ζ11000000000000000000
χ704-4-4444-4-4-22-222-2-22000000−2323000023−2300000000−2i2i2i−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−ζ11000000000000000000
χ714-4-4-44-4444-44-44-4-440000000000000000002-2-220000002-22-2-22-2200000000000000000000000000
χ724-4-4-44-4444-44-44-4-44000000000000000000-222-2000000-22-222-22-200000000000000000000000000
χ734-4-4-44-444-22-22-222-20000000023−23−23230000002-2-22000000−1+31−3−1−31+31−3−1+31+3−1−300000000000000000000000000
χ744-4-4-44-444-22-22-222-20000000023−23−2323000000-222-20000001−3−1+31+3−1−3−1+31−3−1−31+300000000000000000000000000
χ754-4-4-44-444-22-22-222-200000000−232323−230000002-2-22000000−1−31+3−1+31−31+3−1−31−3−1+300000000000000000000000000
χ764-4-4-44-444-22-22-222-200000000−232323−23000000-222-20000001+3−1−31−3−1+3−1−31+3−1+31−300000000000000000000000000
χ77888-88-8-8-8-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000
χ788-888-8-88-8-444-444-4-400000000000000000000000000000000000000000000000000000000000000

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