Finite Group Databasebeta

C2×#356×D47 #26369101

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#356×D47

Splittings

FittingC2×C47×#356 ⋊ C2
SylowC47 ⋊ C22×#356

Subgroups

subgroupG/H
centerC22#99×D47
commutatorC2×C4×C47C23×C4
FrattiniC2×Q8C23×D47
FittingC2×C47×#356C2
socleC22×C47C2×#99
prime radicalC23×D47C22⋊C4
cosocleC2×Q8×C47C24
hypercenterC2×#356D47
hypocenterC47C22×#356
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

1254 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

650 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322391);