Finite Group Databasebeta

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C25×C37×C13⋊C3 #49115236

order36075
automorphism?
homologyAbelianization (H1) = C3×C25×C37 · Schur multiplier (H2) = C1

Aliases

direct productC25×C37×C13⋊C3
unambiguous semidirect productC13⋊(C3×C25×C37)
unambiguous semidirect product(C13×C25)⋊(C3×C37)

Splittings

Fitting, HallC13×C25×C37 ⋊ C3
derived, SylowC13 ⋊ C3×C25×C37
HallC13×C37 ⋊ C3×C25
HallC13×C25 ⋊ C3×C37

Subgroups

subgroupG/H
center, hypercenterC25×C37C13⋊C3
commutator, hypocenterC13C3×C25×C37
FrattiniC5C5×C37×C13⋊C3
FittingC13×C25×C37C3
socleC5×C13×C37C3×C5
prime radicalC5×C37×C13⋊C3C5
cosocleC5×C13C3×C5×C37
LCSG ▷ C13
UCSC1 ◁ C25×C37

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12025

Conjugacy classes & character table

6475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36075, 3);