Finite Group Databasebeta

C2×#22549833 #30647144

order16256
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#22549833

Splittings

FittingC2×#97×C127 ⋊ C2
SylowC127 ⋊ C2×#405

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC2×C127C22×C42
FrattiniC2×C4C23×D127
FittingC2×#97×C127C2
socleC23×C127C22×C4
prime radicalC23×D127C2×C4
cosocleC2×C4×C127C24
hypercenterC2×#97D127
hypocenterC127C2×#405
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C2×#97

592 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 12924);