Finite Group Databasebeta

C42×#10625325 #26214751

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#10625325

Splittings

FittingC42×C8×C47 ⋊ C2
SylowC47 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42D188
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC42×C8×C47C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenterC42×C8D47
hypocenterC47C42×SD16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

1230 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168041);