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C52×C11×C13⋊C3 #24924336

order10725
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×C11×C13⋊C3
unambiguous semidirect productC13⋊(C3×C52×C11)
unambiguous semidirect product(C5×C13)⋊(C3×C5×C11)

Splittings

Fitting, socle, HallC52×C11×C13 ⋊ C3
derived, SylowC13 ⋊ C3×C52×C11
HallC52×C13 ⋊ C3×C11
HallC11×C13 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC52×C11C13⋊C3
commutator, cosocle, hypocenterC13C3×C52×C11
FrattiniC1G
Fitting, socleC52×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C52×C11

64 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 ofC52×C11×D13⋊C3, C52×C11⋊(D13⋊C3), C52×D11×C13⋊C3, …
maximal normal subgroup ofC52×C11×D13⋊C3, C52×C11⋊(D13⋊C3), C52×D11×C13⋊C3, …
maximal quotient ofC2×C52×C11×C13⋊C3, C52×C11×C13⋊C9, C3×C52×C11×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10725, 10);