Finite Group Databasebeta

C2×#22549755 #30641148

order16256
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22549755

Splittings

FittingC24×C4×C127 ⋊ C2
SylowC127 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D127
commutatorC22×C127C23×C4
FrattiniC23C23×D127
FittingC24×C4×C127C2
socleC24×C127C23
prime radicalC23×C22⋊D127C2
cosocleC23×C127C24
hypercenterC24×C4D127
hypocenterC127C2×#386
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C24 ◁ C24×C4

1576 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, 6928);