Finite Group Databasebeta

C2×#22549640 #30638453

order16256
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22549640

Splittings

SylowC127 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D127
commutatorC4×C127C2×C42
FrattiniC22×C4C22×D127
FittingC22×M16×C127C2
socleC23×C127C4⋊C4
prime radicalC24×C127Q8
cosocleC22×C4×C127C23
hypercenterC22×M16D127
hypocenterC127C2×#341
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 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, 4233);