Finite Group Databasebeta

C2×#22550641 #30653438

order16256
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22550641

Splittings

FittingC2×#131×C127 ⋊ C2
SylowC127 ⋊ C2×#568

Subgroups

subgroupG/H
centerC2×C4C23×D127
commutatorC2×C127C24×C4
FrattiniC4C24×D127
FittingC2×#131×C127C2
socleC22×C127C23×C4
prime radicalC2×#41×D127C2
cosocleC4×C127C25
hypercenterC2×#131D127
hypocenterC127C2×#568
LCSG ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C2×#131

1460 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 19218);