Finite Group Databasebeta

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C3×C25×C109⋊C3 #37589249

order24525
automorphism?
homologyAbelianization (H1) = C32×C25 · Schur multiplier (H2) = C3

Aliases

direct productC3×C25×C109⋊C3
unambiguous semidirect productC109⋊(C32×C25)
unambiguous semidirect product(C3×C109)⋊(C3×C25)
unambiguous semidirect product(C25×C109)⋊C32
unambiguous semidirect product(C3×C25×C109)⋊C3

Splittings

FittingC3×C25×C109 ⋊ C3
derived, SylowC109 ⋊ C32×C25
HallC25×C109 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C25C109⋊C3
commutator, hypocenterC109C32×C25
FrattiniC5C3×C5×C109⋊C3
FittingC3×C25×C109C3
socleC3×C5×C109C3×C5
prime radicalC3×C5×C109⋊C3C5
cosocleC5×C109C32×C5
LCSG ▷ C109
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8175

Conjugacy classes & character table

2925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24525, 5);