Finite Group Databasebeta

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C4×C52×C109⋊C3 #45658233

order32700
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52×C109⋊C3
unambiguous semidirect product(C4×C109)⋊(C3×C52)
unambiguous semidirect product(C4×C5×C109)⋊(C3×C5)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC4×C52C109⋊C3
commutator, hypocenterC109C3×C4×C52
FrattiniC2C2×C52×C109⋊C3
FittingC4×C52×C109C3
socleC2×C52×C109C2×C3
prime radicalC2×C52×C109⋊C3C2
cosocleC2×C109C2×C3×C52
LCSG ▷ C109
UCSC1 ◁ C4×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10900

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 69);