Finite Group Databasebeta

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C7×C9×C23⋊C11 #30629967

order15939
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C7×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C23⋊C11
unambiguous semidirect productC23⋊(C7×C9×C11)
unambiguous semidirect product(C9×C23)⋊(C7×C11)
unambiguous semidirect product(C7×C9×C23)⋊C11

Splittings

Fitting, HallC7×C9×C23 ⋊ C11
derived, SylowC23 ⋊ C7×C9×C11
HallC9×C23 ⋊ C7×C11
HallC7×C23 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC7×C9C23⋊C11
commutator, hypocenterC23C7×C9×C11
FrattiniC3C3×C7×C23⋊C11
FittingC7×C9×C23C11
socleC3×C7×C23C3×C11
prime radicalC3×C7×C23⋊C11C3
cosocleC3×C23C3×C7×C11
LCSG ▷ C23
UCSC1 ◁ C7×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1449

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C7×C9×C23⋊C11, C7×C9×AGL(1,𝔽23), C9×D7×C23⋊C11, …
maximal normal subgroup ofC2×C7×C9×C23⋊C11, C7×C9×AGL(1,𝔽23), C9×D7×C23⋊C11, …
maximal quotient ofC2×C7×C9×C23⋊C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15939, 2);