Finite Group Databasebeta

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C3×D11×C71⋊C7 #45659028

order32802
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×D11×C71⋊C7
unambiguous semidirect productC11⋊(C2×C3×C71⋊C7)
unambiguous semidirect product(D11×C71)⋊(C3×C7)
unambiguous semidirect product(C3×D11×C71)⋊C7

Splittings

Fitting, socle, HallC3×C11×C71 ⋊ C2×C7
derived, HallC11×C71 ⋊ C2×C3×C7
HallC3×C11×C71⋊C7 ⋊ C2
HallC11×C71⋊C7 ⋊ C2×C3
HallC3×D11×C71 ⋊ C7
HallD11×C71 ⋊ C3×C7
HallC3×C71 ⋊ C7×D11
SylowC71 ⋊ C3×C7×D11
HallC3×C11 ⋊ C2×C71⋊C7
SylowC11 ⋊ C2×C3×C71⋊C7

Subgroups

subgroupG/H
center, hypercenterC3D11×C71⋊C7
commutator, cosocle, hypocenterC11×C71C2×C3×C7
FrattiniC1G
Fitting, socleC3×C11×C71C2×C7
LCSG ▷ C11×C71
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32802, 20);