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C3×C13×C11⋊C25 #24924328

order10725
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C3×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×C11⋊C25
unambiguous semidirect productC11⋊(C3×C13×C25)
unambiguous semidirect product(C3×C11)⋊(C13×C25)
unambiguous semidirect product(C3×C11×C13)⋊C25

Splittings

derived, SylowC11 ⋊ C3×C13×C25
HallC3×C11×C13 ⋊ C25
HallC11×C13 ⋊ C3×C25
HallC3×C11 ⋊ C13×C25

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13C11⋊C5
commutator, hypocenterC11C3×C13×C25
FrattiniC5C3×C13×C11⋊C5
Fitting, socle, prime radicalC3×C5×C11×C13C5
cosocleC5×C11C3×C5×C13
LCSG ▷ C11
UCSC1 ◁ C3×C5×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C13×C11⋊C25, C3×D13×C11⋊C25, C3×C13×D11⋊C25, …
maximal normal subgroup ofC2×C3×C13×C11⋊C25, C3×D13×C11⋊C25, C3×C13×D11⋊C25, …
maximal quotient ofC2×C3×C13×C11⋊C25, C9×C13×C11⋊C25, C32×C13×C11⋊C25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10725, 2);