Finite Group Databasebeta

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C4×#22582837 #49097643

order35968
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#22582837

Splittings

FittingC4×C4⋊C4×C281 ⋊ C2
SylowC281 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D281
commutatorC2×C281C22×C42
FrattiniC23C23×D281
FittingC4×C4⋊C4×C281C2
socle, cosocleC23×C281C24
prime radicalC23×D281C23
hypercenterC4×C4⋊C4D281
hypocenterC281C4×#117
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

5680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6850);