Finite Group Databasebeta

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C13×C25×C37⋊C3 #49115235

order36075
automorphism?
homologyAbelianization (H1) = C3×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC13×C25×C37⋊C3
unambiguous semidirect productC37⋊(C3×C13×C25)
unambiguous semidirect product(C25×C37)⋊(C3×C13)

Splittings

Fitting, HallC13×C25×C37 ⋊ C3
derived, SylowC37 ⋊ C3×C13×C25
HallC25×C37 ⋊ C3×C13
HallC13×C37 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC13×C25C37⋊C3
commutator, hypocenterC37C3×C13×C25
FrattiniC5C5×C13×C37⋊C3
FittingC13×C25×C37C3
socleC5×C13×C37C3×C5
prime radicalC5×C13×C37⋊C3C5
cosocleC5×C37C3×C5×C13
LCSG ▷ C37
UCSC1 ◁ C13×C25

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12025

Conjugacy classes & character table

4875 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36075, 2);