Finite Group Databasebeta

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C4×C41×C13⋊C9 #34062850

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

Aliases

direct productC4×C41×C13⋊C9
unambiguous semidirect product(C4×C13)⋊(C9×C41)
unambiguous semidirect product(C4×C13×C41)⋊C9

Splittings

derived, SylowC13 ⋊ C4×C9×C41
HallC4×C13×C41 ⋊ C9
HallC13×C41 ⋊ C4×C9
HallC4×C13 ⋊ C9×C41

Subgroups

subgroupG/H
center, hypercenterC3×C4×C41C13⋊C3
commutator, hypocenterC13C4×C9×C41
FrattiniC2×C3C2×C13⋊C3×C41
FittingC3×C4×C13×C41C3
socle, prime radicalC2×C3×C13×C41C2×C3
cosocleC2×C3×C13C2×C3×C41
LCSG ▷ C13
UCSC1 ◁ C3×C4×C41

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19188

Conjugacy classes & character table

3444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 2);