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C5×C43×C11⋊C5 #26044787

order11825
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C52×C43 · Schur multiplier (H2) = C5

Aliases

direct productC5×C43×C11⋊C5
unambiguous semidirect productC11⋊(C52×C43)
unambiguous semidirect product(C5×C11)⋊(C5×C43)
unambiguous semidirect product(C11×C43)⋊C52
unambiguous semidirect product(C5×C11×C43)⋊C5

Splittings

Fitting, socleC5×C11×C43 ⋊ C5
derived, SylowC11 ⋊ C52×C43
HallC11×C43 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5×C43C11⋊C5
commutator, cosocle, hypocenterC11C52×C43
FrattiniC1G
Fitting, socleC5×C11×C43C5
LCSG ▷ C11
UCSC1 ◁ C5×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1505 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C43×AGL(1,𝔽11), C5×C43⋊AGL(1,𝔽11), C5×C11⋊C5×D43, …
maximal normal subgroup ofC5×C43×AGL(1,𝔽11), C5×C43⋊AGL(1,𝔽11), C5×C11⋊C5×D43, …
maximal quotient ofC2×C5×C43×C11⋊C5, C3×C5×C43×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11825, 4);