Finite Group Databasebeta

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C4×C52⋊(C109⋊C3) #45658231

order32700
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52⋊(C109⋊C3)
unambiguous semidirect product(C4×C52)⋊(C109⋊C3)
unambiguous semidirect product(C4×C109)⋊(C52⋊C3)

Splittings

Fitting, HallC4×C52×C109 ⋊ C3
derived, HallC52×C109 ⋊ C3×C4
HallC4×C109 ⋊ C52⋊C3
SylowC109 ⋊ C4×C52⋊C3
HallC4×C52 ⋊ C109⋊C3
SylowC52 ⋊ C4×C109⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C52⋊(C109⋊C3)
commutator, hypocenterC52×C109C3×C4
FrattiniC2C2×C52⋊(C109⋊C3)
FittingC4×C52×C109C3
socle, cosocleC2×C52×C109C2×C3
prime radicalC2×C52⋊(C109⋊C3)C2
LCSG ▷ C52×C109
UCSC1 ◁ C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6540

Conjugacy classes & character table

3644 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 67);