Finite Group Databasebeta

C2×#22549933 #30647351

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22549933

Splittings

SylowC127 ⋊ C2×#432

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutatorC22×C127C23×C4
FrattiniC2×C4C23×D127
FittingC22×C42×C127C2
socleC23×C127C22×C4
prime radicalC24×C127C2×C4
cosocleC2×C4×C127C24
hypercenterC22×C42D127
hypocenterC127C2×#432
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C22×C42

488 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13131);