Finite Group Databasebeta

C2×#22550413 #30651999

order16256
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22550413

Splittings

FittingC2×C4×Q8×C127 ⋊ C2
SylowC127 ⋊ C2×#529

Subgroups

subgroupG/H
centerC22×C4C22×D127
commutator, cosocleC22×C127C25
FrattiniC22C24×D127
FittingC2×C4×Q8×C127C2
socleC23×C127C24
prime radicalC2×#16861184C2
hypercenterC2×C4×Q8D127
hypocenterC127C2×#529
LCSG ▷ C22×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

1232 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 17779);