Finite Group Databasebeta

← Prev (#16808146) Next (#16808148) →

C22×#11719098 #16808147

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11719098
unambiguous semidirect productD13⋊(C2×#428)

Splittings

FittingC22×C13×M16 ⋊ C4
SylowC13 ⋊ C22×#428

Subgroups

subgroupG/H
centerC23C2×C4⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC22×C13×M16C4
socleC23×C13C2×C4⋊C4
prime radicalC24×D13D4
cosocleC4×D13C25
hypercenterC22×M16#261
hypocenterC13C22×#428
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

3182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114796);