Finite Group Databasebeta

C2×#22549927 #30647344

order16256
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#22549927

Splittings

FittingC2×C4×C8×C127 ⋊ C2
SylowC127 ⋊ C2×#431

Subgroups

subgroupG/H
centerC2×C42C2×D127
commutatorC2×C127C23×C8
FrattiniC2×C4C23×D127
FittingC2×C4×C8×C127C2
socleC23×C127C22×C4
prime radicalC23×D127C2×C4
cosocleC2×C4×C127C24
hypercenterC2×C4×C8D127
hypocenterC127C2×#431
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

528 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 13124);