Finite Group Databasebeta

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C4⋊C4×C22⋊D281 #49098202

order35968
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×C22⋊D281

Splittings

FittingC22×C4⋊C4×C281 ⋊ C2
SylowC281 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D281
commutatorC22×C281C23×C4
FittingC22×C4⋊C4×C281C2
socle, cosocleC23×C281C24
prime radicalC22×C22⋊D281C22
hypercenterC22×C4⋊C4D281
hypocenterC281D4×C4⋊C4
LCSG ▷ C22×C281 ▷ C281
UCSC1 ◁ C23 ◁ C22×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

5650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 7409);