Finite Group Databasebeta

← Prev (#22547555) Next (#22547557) →

C5×C29×C11⋊C5 #22547556

order7975
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C52×C29 · Schur multiplier (H2) = C5

Aliases

direct productC5×C29×C11⋊C5
unambiguous semidirect productC11⋊(C52×C29)
unambiguous semidirect product(C5×C11)⋊(C5×C29)
unambiguous semidirect product(C11×C29)⋊C52
unambiguous semidirect product(C5×C11×C29)⋊C5

Splittings

Fitting, socleC5×C11×C29 ⋊ C5
derived, SylowC11 ⋊ C52×C29
HallC11×C29 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5×C29C11⋊C5
commutator, hypocenterC11C52×C29
FrattiniC1G
Fitting, socleC5×C11×C29C5
LCSG ▷ C11
UCSC1 ◁ C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C29×AGL(1,𝔽11), C5×C29⋊AGL(1,𝔽11), C5×C11⋊C5×D29, …
maximal normal subgroup ofC5×C29×AGL(1,𝔽11), C5×C29⋊AGL(1,𝔽11), C5×C11⋊C5×D29, …
maximal quotient ofC2×C5×C29×C11⋊C5, C3×C5×C29×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7975, 4);