Finite Group Databasebeta

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C22×#11763756 #17978880

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC22×#11763756
unambiguous semidirect productD17⋊(C2×#385)

Splittings

FittingC22×C22⋊C4×C17 ⋊ C4
SylowC17 ⋊ C22×#385

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC22×C22⋊C4×C17C4
socleC24×C17C22×C4
prime radicalC25×D17C22
cosocleC22×D17C25
hypercenterC22×C22⋊C4#595
hypocenterC17C22×#385
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C22⋊C4

8670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114124);