Finite Group Databasebeta

C8×#13094053 #26185698

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#13094053

Splittings

FittingC8×SD16×C47 ⋊ C2
SylowC47 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C8D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC8×SD16×C47C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625352C2×C4
cosocleC42×C47C24
hypercenterC8×SD16D47
hypocenterC47C8×#137
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×SD16

714 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138988);