Finite Group Databasebeta

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C22×#11719070 #16807475

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#11719070
unambiguous semidirect productD13⋊(C2×#385)

Splittings

FittingC22×C13×C22⋊C4 ⋊ C4
SylowC13 ⋊ C22×#385

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC22×C13C24×C4
FrattiniC22C24×#261
FittingC22×C13×C22⋊C4C4
socleC24×C13C22×C4
prime radicalC25×D13C22
cosocleC22×D13C25
hypercenterC22×C22⋊C4#261
hypocenterC13C22×#385
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊C4

8670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114124);