Finite Group Databasebeta

← Group #11715654

Character table — Group #11715654

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111133336666121212121212121212122424242432323232111133336666121212121212121212122424242432323232
order1244224422442444444444888836121222442244224424444444448888661212
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ311-1-111-1-1-1-111-11iiii−i−i−i−ii−ii−i11-1-111-1-111-1-1-1-111-11iiii−i−i−i−ii−ii−i11-1-1
χ411-1-111-1-1-1-111-11−i−i−i−iiiii−ii−ii11-1-111-1-111-1-1-1-111-11−i−i−i−iiiii−ii−ii11-1-1
χ522222222222222000000000000-1-1-1-122222222222222000000000000-1-1-1-1
χ622-2-222-2-2-2-222-22000000000000-1-11122-2-222-2-2-2-222-22000000000000-1-111
χ72-22i−2i2-22i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000-11i−i2-22i−2i2-22i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000-11i−i
χ82-22i−2i2-22i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000-11i−i2-22i−2i2-22i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000-11i−i
χ92-2−2i2i2-2−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000-11−ii2-2−2i2i2-2−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000-11−ii
χ102-2−2i2i2-2−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000-11−ii2-2−2i2i2-2−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000-11−ii
χ1133333333-1-1-1-1-1-111111111-1-1-1-1000033333333-1-1-1-1-1-111111111-1-1-1-10000
χ1233333333-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000033333333-1-1-1-1-1-1-1-1-1-1-1-1-1-111110000
χ133333-1-1-1-13-13-1-1-11-11-11-11-111-1-100003333-1-1-1-13-13-1-1-11-11-11-11-111-1-10000
χ143333-1-1-1-13-13-1-1-1-11-11-11-11-1-11100003333-1-1-1-13-13-1-1-1-11-11-11-11-1-1110000
χ153333-1-1-1-1-13-13-1-11-11-11-11-1-1-11100003333-1-1-1-1-13-13-1-11-11-11-11-1-1-1110000
χ163333-1-1-1-1-13-13-1-1-11-11-11-1111-1-100003333-1-1-1-1-13-13-1-1-11-11-11-1111-1-10000
χ1733-3-333-3-311-1-11-1iiii−i−i−i−i−ii−ii000033-3-333-3-311-1-11-1iiii−i−i−i−i−ii−ii0000
χ1833-3-333-3-311-1-11-1−i−i−i−iiiiii−ii−i000033-3-333-3-311-1-11-1−i−i−i−iiiiii−ii−i0000
χ1933-3-3-1-1111-3-131-1i−ii−i−ii−ii−iii−i000033-3-3-1-1111-3-131-1i−ii−i−ii−ii−iii−i0000
χ2033-3-3-1-1111-3-131-1−ii−iii−ii−ii−i−ii000033-3-3-1-1111-3-131-1−ii−iii−ii−ii−i−ii0000
χ2133-3-3-1-111-313-11-1i−ii−i−ii−iii−i−ii000033-3-3-1-111-313-11-1i−ii−i−ii−iii−i−ii0000
χ2233-3-3-1-111-313-11-1−ii−iii−ii−i−iii−i000033-3-3-1-111-313-11-1−ii−iii−ii−i−iii−i0000
χ234-44i−4i4-44i−4i0000000000000000001-1−ii4-44i−4i4-44i−4i0000000000000000001-1−ii
χ244-4−4i4i4-4−4i4i0000000000000000001-1i−i4-4−4i4i4-4−4i4i0000000000000000001-1i−i
χ256666-2-2-2-2-2-2-2-22200000000000000006666-2-2-2-2-2-2-2-2220000000000000000
χ2666-6-6-2-22222-2-2-22000000000000000066-6-6-2-22222-2-2-220000000000000000
χ276-66i−6i-22−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000006-66i−6i-22−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ286-66i−6i-22−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000006-66i−6i-22−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ296-6−6i6i-222i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000006-6−6i6i-222i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ306-6−6i6i-222i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000006-6−6i6i-222i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3211111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ3311-1-111-1-1-1-111-11iiii−i−i−i−ii−ii−i11-1-1-1-111-1-11111-1-11-1−i−i−i−iiiii−ii−ii-1-111
χ3411-1-111-1-1-1-111-11−i−i−i−iiiii−ii−ii11-1-1-1-111-1-11111-1-11-1iiii−i−i−i−ii−ii−i-1-111
χ3522222222222222000000000000-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000001111
χ3622-2-222-2-2-2-222-22000000000000-1-111-2-222-2-22222-2-22-200000000000011-1-1
χ372-22i−2i2-22i−2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000-11i−i-22−2i2i-22−2i2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00001-1−ii
χ382-22i−2i2-22i−2i000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000-11i−i-22−2i2i-22−2i2i0000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00001-1−ii
χ392-2−2i2i2-2−2i2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000-11−ii-222i−2i-222i−2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00001-1i−i
χ402-2−2i2i2-2−2i2i000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000-11−ii-222i−2i-222i−2i0000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00001-1i−i
χ4133333333-1-1-1-1-1-111111111-1-1-1-10000-3-3-3-3-3-3-3-3111111-1-1-1-1-1-1-1-111110000
χ4233333333-1-1-1-1-1-1-1-1-1-1-1-1-1-111110000-3-3-3-3-3-3-3-311111111111111-1-1-1-10000
χ433333-1-1-1-13-13-1-1-11-11-11-11-111-1-10000-3-3-3-31111-31-3111-11-11-11-11-1-1110000
χ443333-1-1-1-13-13-1-1-1-11-11-11-11-1-1110000-3-3-3-31111-31-31111-11-11-11-111-1-10000
χ453333-1-1-1-1-13-13-1-11-11-11-11-1-1-1110000-3-3-3-311111-31-311-11-11-11-1111-1-10000
χ463333-1-1-1-1-13-13-1-1-11-11-11-1111-1-10000-3-3-3-311111-31-3111-11-11-11-1-1-1110000
χ4733-3-333-3-311-1-11-1iiii−i−i−i−i−ii−ii0000-3-333-3-333-1-111-11−i−i−i−iiiiii−ii−i0000
χ4833-3-333-3-311-1-11-1−i−i−i−iiiiii−ii−i0000-3-333-3-333-1-111-11iiii−i−i−i−i−ii−ii0000
χ4933-3-3-1-1111-3-131-1i−ii−i−ii−ii−iii−i0000-3-33311-1-1-131-3-11−ii−iii−ii−ii−i−ii0000
χ5033-3-3-1-1111-3-131-1−ii−iii−ii−ii−i−ii0000-3-33311-1-1-131-3-11i−ii−i−ii−ii−iii−i0000
χ5133-3-3-1-111-313-11-1i−ii−i−ii−iii−i−ii0000-3-33311-1-13-1-31-11−ii−iii−ii−i−iii−i0000
χ5233-3-3-1-111-313-11-1−ii−iii−ii−i−iii−i0000-3-33311-1-13-1-31-11i−ii−i−ii−iii−i−ii0000
χ534-44i−4i4-44i−4i0000000000000000001-1−ii-44−4i4i-44−4i4i000000000000000000-11i−i
χ544-4−4i4i4-4−4i4i0000000000000000001-1i−i-444i−4i-444i−4i000000000000000000-11−ii
χ556666-2-2-2-2-2-2-2-2220000000000000000-6-6-6-622222222-2-20000000000000000
χ5666-6-6-2-22222-2-2-220000000000000000-6-66622-2-2-2-2222-20000000000000000
χ576-66i−6i-22−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000-66−6i6i2-22i−2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ586-66i−6i-22−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000-66−6i6i2-22i−2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ596-6−6i6i-222i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000-666i−6i2-2−2i2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ606-6−6i6i-222i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000-666i−6i2-2−2i2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000

Here i is the imaginary unit (i² = −1).