Finite Group Databasebeta

C8×M16×D47 #26181848

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×M16×D47

Splittings

FittingC8×M16×C47 ⋊ C2
SylowC47 ⋊ C2×C8×M16

Subgroups

subgroupG/H
centerC4×C8C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC42C23×D47
FittingC8×M16×C47C2
socleC22×C47C22×C42
prime radicalC23×D47C42
cosocleC42×C47C24
hypercenterC8×M16D47
hypocenterC47C2×C8×M16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ C8×M16

1046 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135138);