Finite Group Databasebeta

C2×#22549918 #30647315

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

Aliases

direct productC2×#22549918

Splittings

SylowC127 ⋊ C2×#428

Subgroups

subgroupG/H
centerC23C2×D508
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
FittingC22×M16×C127C2
socleC23×C127C2×D4
prime radicalC24×C127D4
cosocleC2×C4×C127C24
hypercenterC22×M16D127
hypocenterC127C2×#428
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

536 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, 13095);