Finite Group Databasebeta

C2×#22549849 #30647186

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

Aliases

direct productC2×#22549849

Splittings

FittingC2×#117×C127 ⋊ C2
SylowC127 ⋊ C2×#410

Subgroups

subgroupG/H
centerC2×C4(C2×D127)⋊C4
commutatorC22×C127C23×C4
FrattiniC23C23×D127
FittingC2×#117×C127C2
socleC22×C127C2×C22⋊C4
prime radicalC22×#14523248C2
cosocleC23×C127C24
hypercenterC2×#117D127
hypocenterC127C2×#410
LCSG ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

788 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, 12966);