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C2×C9×C13×D41 #34062894

order19188
automorphism?
homologyAbelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C13×D41
unambiguous semidirect productC41⋊(C22×C9×C13)
unambiguous semidirect product(C2×C41)⋊(C2×C9×C13)

Splittings

FittingC2×C9×C13×C41 ⋊ C2
derived, SylowC41 ⋊ C22×C9×C13
HallC9×C13×C41 ⋊ C22
HallC13×C41 ⋊ C22×C9
HallC9×C41 ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC2×C9×C13D41
commutator, hypocenterC41C22×C9×C13
FrattiniC3C2×C3×C13×D41
FittingC2×C9×C13×C41C2
socleC2×C3×C13×C41C2×C3
prime radicalC2×C3×C13×D41C3
cosocleC3×C41C22×C3×C13
LCSG ▷ C41
UCSC1 ◁ C2×C9×C13

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9594

Conjugacy classes & character table

5148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 46);