Finite Group Databasebeta

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A4×C25×C109 #45658208

order32700
automorphism?
homologyAbelianization (H1) = C3×C25×C109 · Schur multiplier (H2) = C2

Aliases

direct productA4×C25×C109
unambiguous semidirect productC22⋊(C3×C25×C109)
unambiguous semidirect product(C22×C25)⋊(C3×C109)

Splittings

Fitting, HallC22×C25×C109 ⋊ C3
derived, SylowC22 ⋊ C3×C25×C109
HallC22×C109 ⋊ C3×C25
HallC22×C25 ⋊ C3×C109

Subgroups

subgroupG/H
center, hypercenterC25×C109A4
commutator, hypocenterC22C3×C25×C109
FrattiniC5C5×A4×C109
FittingC22×C25×C109C3
socleC22×C5×C109C3×C5
prime radicalC5×A4×C109C5
cosocleC22×C5C3×C5×C109
LCSG ▷ C22
UCSC1 ◁ C25×C109

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10900

Conjugacy classes & character table

10900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 44);