Finite Group Databasebeta

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C11×C29×C52⋊C3 #37560830

order23925
automorphism?
homologyAbelianization (H1) = C3×C11×C29 · Schur multiplier (H2) = C5

Aliases

direct productC11×C29×C52⋊C3
unambiguous semidirect productC52⋊(C3×C11×C29)
unambiguous semidirect product(C52×C11)⋊(C3×C29)
unambiguous semidirect product(C52×C29)⋊(C3×C11)
unambiguous semidirect product(C52×C11×C29)⋊C3

Splittings

Fitting, socle, HallC52×C11×C29 ⋊ C3
derived, SylowC52 ⋊ C3×C11×C29
HallC52×C29 ⋊ C3×C11
HallC52×C11 ⋊ C3×C29

Subgroups

subgroupG/H
center, hypercenterC11×C29C52⋊C3
commutator, cosocle, hypocenterC52C3×C11×C29
FrattiniC1G
Fitting, socleC52×C11×C29C3
LCSG ▷ C52
UCSC1 ◁ C11×C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

3509 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23925, 5);