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C11×C25×C13⋊C3 #24924329

order10725
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×C13⋊C3
unambiguous semidirect productC13⋊(C3×C11×C25)
unambiguous semidirect product(C13×C25)⋊(C3×C11)
unambiguous semidirect product(C11×C13×C25)⋊C3

Splittings

Fitting, HallC11×C13×C25 ⋊ C3
derived, SylowC13 ⋊ C3×C11×C25
HallC13×C25 ⋊ C3×C11
HallC11×C13 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25C13⋊C3
commutator, hypocenterC13C3×C11×C25
FrattiniC5C5×C11×C13⋊C3
FittingC11×C13×C25C3
socleC5×C11×C13C3×C5
prime radicalC5×C11×C13⋊C3C5
cosocleC5×C13C3×C5×C11
LCSG ▷ C13
UCSC1 ◁ C11×C25

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C25×C13⋊C3, C11×C25×D13⋊C3, D11×C25×C13⋊C3, …
maximal normal subgroup ofC2×C11×C25×C13⋊C3, C11×C25×D13⋊C3, D11×C25×C13⋊C3, …
maximal quotient ofC2×C11×C25×C13⋊C3, C11×C25×C13⋊C9, C3×C11×C25×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10725, 3);