Finite Group Databasebeta

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C4×#11763661 #17952044

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11763661

Splittings

FittingC4×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C4×#327

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#10587581C22
cosocleC22×C4×D17C23
hypercenterC4×C4⋊C4#595
hypocenterC17C4×#327
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1087288);