Finite Group Databasebeta

C2×#30656505 #45664055

order32896
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#30656505

Splittings

SylowC257 ⋊ C2×#343

Subgroups

subgroupG/H
centerC23#16861595
commutatorC22×C257C2×C42
FrattiniC22×C4C22×D257
FittingC22×M16×C257C2
socleC23×C257C22⋊C4
prime radicalC24×C257C2×C4
cosocleC22×C4×C257C23
hypercenterC22×M16D257
hypocenterC257C2×#343
LCSG ▷ C22×C257 ▷ C2×C257 ▷ C257
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

432 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, 4245);