Finite Group Databasebeta

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C3×C25×C163⋊C3 #49144164

order36675
automorphism?
homologyAbelianization (H1) = C32×C25 · Schur multiplier (H2) = C3

Aliases

direct productC3×C25×C163⋊C3
unambiguous semidirect productC163⋊(C32×C25)
unambiguous semidirect product(C3×C163)⋊(C3×C25)
unambiguous semidirect product(C25×C163)⋊C32
unambiguous semidirect product(C3×C25×C163)⋊C3

Splittings

FittingC3×C25×C163 ⋊ C3
derived, SylowC163 ⋊ C32×C25
HallC25×C163 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C25C163⋊C3
commutator, hypocenterC163C32×C25
FrattiniC5C3×C5×C163⋊C3
FittingC3×C25×C163C3
socleC3×C5×C163C3×C5
prime radicalC3×C5×C163⋊C3C5
cosocleC5×C163C32×C5
LCSG ▷ C163
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12225

Conjugacy classes & character table

4275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36675, 5);