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C11×C23×C7⋊C9 #30629968

order15939
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C9×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC11×C23×C7⋊C9
unambiguous semidirect productC7⋊(C9×C11×C23)
unambiguous semidirect product(C7×C11)⋊(C9×C23)
unambiguous semidirect product(C7×C11×C23)⋊C9

Splittings

derived, SylowC7 ⋊ C9×C11×C23
HallC7×C11×C23 ⋊ C9
HallC7×C23 ⋊ C9×C11
HallC7×C11 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC3×C11×C23ΓL(1,𝔽8)
commutator, hypocenterC7C9×C11×C23
FrattiniC3C11×ΓL(1,𝔽8)×C23
Fitting, socle, prime radicalC3×C7×C11×C23C3
cosocleC3×C7C3×C11×C23
LCSG ▷ C7
UCSC1 ◁ C3×C11×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15939

Conjugacy classes & character table

3795 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C23×C7⋊C9, C11×D23×C7⋊C9, D11×C23×C7⋊C9, …
maximal normal subgroup ofC2×C11×C23×C7⋊C9, C11×D23×C7⋊C9, D11×C23×C7⋊C9, …
maximal quotient ofC2×C11×C23×C7⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15939, 3);