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C9×C13×#4223 #34062872

order19188
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×C13×#4223

Splittings

Fitting, HallC9×C13×C41 ⋊ C4
derived, SylowC41 ⋊ C4×C9×C13
HallC13×C41 ⋊ C4×C9
HallC9×C41 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC9×C13#4223
commutator, hypocenterC41C4×C9×C13
FrattiniC3C3×C13×#4223
FittingC9×C13×C41C4
socleC3×C13×C41C3×C4
prime radicalC3×C13×D41C2×C3
cosocleC3×D41C2×C3×C13
LCSG ▷ C41
UCSC1 ◁ C9×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4797

Conjugacy classes & character table

1638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 24);