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C7×(C13⋊C3)⋊D41 #36375608

order22386
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C13⋊C3)⋊D41
unambiguous semidirect product(C13⋊C3)⋊(C7×D41)
unambiguous semidirect productC41⋊(C7×D13⋊C3)
unambiguous semidirect productD533⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C41 ⋊ C2×C3
derived, HallC13×C41 ⋊ C2×C3×C7
HallC7×C13⋊C3×C41 ⋊ C2
HallC7×D533 ⋊ C3
HallC13⋊C3×C41 ⋊ C2×C7
HallD533 ⋊ C3×C7
HallC7×C41 ⋊ D13⋊C3
HallC7×C13⋊C3 ⋊ D41
HallC7×C13 ⋊ C3×D41
SylowC41 ⋊ C7×D13⋊C3
HallC13⋊C3 ⋊ C7×D41
SylowC13 ⋊ C3×C7×D41

Subgroups

subgroupG/H
center, hypercenterC7(C13⋊C3)⋊D41
commutator, cosocle, hypocenterC13×C41C2×C3×C7
FrattiniC1G
Fitting, socleC7×C13×C41C2×C3
LCSG ▷ C13×C41
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3731

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22386, 29);