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C9×C41×#261 #34062873

order19188
automorphism?
homologyAbelianization (H1) = C4×C9×C41 · Schur multiplier (H2) = C1

Aliases

direct productC9×C41×#261

Splittings

Fitting, HallC9×C13×C41 ⋊ C4
derived, SylowC13 ⋊ C4×C9×C41
HallC13×C41 ⋊ C4×C9
HallC9×C13 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC9×C41#261
commutator, hypocenterC13C4×C9×C41
FrattiniC3C3×C41×#261
FittingC9×C13×C41C4
socleC3×C13×C41C3×C4
prime radicalC3×D13×C41C2×C3
cosocleC3×D13C2×C3×C41
LCSG ▷ C13
UCSC1 ◁ C9×C41

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4797

Conjugacy classes & character table

2583 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 25);