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C13⋊C3×C11⋊C25 #24924330

order10725
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, HallC11×C13 ⋊ C3×C25
HallC13×C11⋊C25 ⋊ C3
HallC11×C13⋊C3 ⋊ C25
SylowC13 ⋊ C3×C11⋊C25
SylowC11 ⋊ C25×C13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC5C13⋊C3×C11⋊C5
commutator, hypocenterC11×C13C3×C25
Fitting, socle, cosocleC5×C11×C13C3×C5
prime radicalC5×C11×C13⋊C3C5
LCSG ▷ C11×C13
UCSC1 ◁ C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10725, 4);