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C3×C25×C37⋊C3 #22552264

order8325
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C32×C25 · Schur multiplier (H2) = C3

Aliases

direct productC3×C25×C37⋊C3
unambiguous semidirect productC37⋊(C32×C25)
unambiguous semidirect product(C3×C37)⋊(C3×C25)
unambiguous semidirect product(C25×C37)⋊C32
unambiguous semidirect product(C3×C25×C37)⋊C3

Splittings

FittingC3×C25×C37 ⋊ C3
derived, SylowC37 ⋊ C32×C25
HallC25×C37 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C25C37⋊C3
commutator, hypocenterC37C32×C25
FrattiniC5C3×C5×C37⋊C3
FittingC3×C25×C37C3
socleC3×C5×C37C3×C5
LCSG ▷ C37
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1125 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C25×D37⋊C3, C3×C25⋊(D37⋊C3), C3×D25×C37⋊C3, …
maximal normal subgroup ofC3×C25×D37⋊C3, C3×C25⋊(D37⋊C3), C3×D25×C37⋊C3, …
maximal quotient ofC2×C3×C25×C37⋊C3, A4×C25×C37⋊C3, C3×C25×C22⋊(C37⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8325, 5);