Finite Group Databasebeta

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C22×#11763820 #17979552

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11763820
unambiguous semidirect productD17⋊(C2×#428)

Splittings

FittingC22×M16×C17 ⋊ C4
SylowC17 ⋊ C22×#428

Subgroups

subgroupG/H
centerC23C2×C4⋊#595
commutatorC4×C17C24×C4
FrattiniC4C24×#595
FittingC22×M16×C17C4
socleC23×C17C2×C4⋊C4
prime radicalC24×D17D4
cosocleC4×D17C25
hypercenterC22×M16#595
hypocenterC17C22×#428
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

3182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114796);