Finite Group Databasebeta

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C5×C29×C23⋊C11 #49144232

order36685
automorphism?
homologyAbelianization (H1) = C5×C11×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×C29×C23⋊C11
unambiguous semidirect productC23⋊(C5×C11×C29)
unambiguous semidirect product(C5×C23)⋊(C11×C29)
unambiguous semidirect product(C23×C29)⋊(C5×C11)
unambiguous semidirect product(C5×C23×C29)⋊C11

Splittings

Fitting, socle, HallC5×C23×C29 ⋊ C11
derived, SylowC23 ⋊ C5×C11×C29
HallC23×C29 ⋊ C5×C11
HallC5×C23 ⋊ C11×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29C23⋊C11
commutator, cosocle, hypocenterC23C5×C11×C29
FrattiniC1G
Fitting, socleC5×C23×C29C11
LCSG ▷ C23
UCSC1 ◁ C5×C29

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3335

Conjugacy classes & character table

1885 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36685, 2);