Finite Group Databasebeta

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C4×#11763686 #17956637

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11763686

Splittings

FittingC4×C22⋊C4×C17 ⋊ C4
SylowC17 ⋊ C4×#342

Subgroups

subgroupG/H
centerC2×C4(C2×#595)⋊C4
commutatorC22×C17C43
FrattiniC24C22×#595
FittingC4×C22⋊C4×C17C4
socleC22×C17C2×#95
prime radical, cosocleC24×D17C23
hypercenterC4×C22⋊C4#595
hypocenterC17C4×#342
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

1482 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, 1091881);