Finite Group Databasebeta

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C9×C23×D41 #30684056

order16974
isoclinismisoclinic class of D41
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC9×C23×D41
unambiguous semidirect productC41⋊(C2×C9×C23)

Splittings

Fitting, HallC9×C23×C41 ⋊ C2
derived, SylowC41 ⋊ C2×C9×C23
HallC23×C41 ⋊ C2×C9
HallC9×C41 ⋊ C2×C23

Subgroups

subgroupG/H
center, hypercenterC9×C23D41
commutator, hypocenterC41C2×C9×C23
FrattiniC3C3×C23×D41
FittingC9×C23×C41C2
socleC3×C23×C41C2×C3
prime radicalC3×C23×D41C3
cosocleC3×C41C2×C3×C23
LCSG ▷ C41
UCSC1 ◁ C9×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8487

Conjugacy classes & character table

4554 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C23×#4223, C9×C23⋊#4223, C9×D23×D41, …
maximal normal subgroup ofC9×C23×#4223, C9×C23⋊#4223, C9×D23×D41, …
maximal quotient ofC9×C23×Dic41, C2×C9×C23×D41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16974, 2);