Finite Group Databasebeta

C2×#22549792 #30641935

order16256
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22549792

Splittings

FittingC22×C22⋊C4×C127 ⋊ C2
SylowC127 ⋊ C2×#394

Subgroups

subgroupG/H
centerC24C22×D127
commutator, cosocleC23×C127C24
FrattiniC23C23×D127
FittingC22×C22⋊C4×C127C2
socleC24×C127C23
prime radicalC23×C22⋊D127C2
hypercenterC22×C22⋊C4D127
hypocenterC127C2×#394
LCSG ▷ C23×C127 ▷ C127
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 7715);