Finite Group Databasebeta

C2×#30656665 #45667547

order32896
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#30656665

Splittings

SylowC257 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D257
commutator, cosocleC23×C257C24
FrattiniC23C23×D257
FittingC22×C22⋊C4×C257C2
socleC24×C257C23
prime radicalC25×C257C22
hypercenterC22×C22⋊C4D257
hypocenterC257C2×#397
LCSG ▷ C23×C257 ▷ C257
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16448

Conjugacy classes & character table

5164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 7737);