Finite Group Databasebeta

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C2×C11×D71⋊C7 #36346125

order21868
automorphism?
homologyAbelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D71⋊C7
unambiguous semidirect productD71⋊(C2×C7×C11)
unambiguous semidirect product(C2×D71)⋊(C7×C11)
unambiguous semidirect product(C71⋊C7)⋊(C22×C11)
unambiguous semidirect product(C2×C71⋊C7)⋊(C2×C11)
unambiguous semidirect product(C2×C11×D71)⋊C7

Splittings

Fitting, socleC2×C11×C71 ⋊ C2×C7
derived, SylowC71 ⋊ C22×C7×C11
HallC11×C71⋊C7 ⋊ C22
HallC2×C11×D71 ⋊ C7
HallC11×C71 ⋊ C22×C7
HallC71⋊C7 ⋊ C22×C11
HallC2×D71 ⋊ C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D71⋊C7
commutator, cosocle, hypocenterC71C22×C7×C11
FrattiniC1G
Fitting, socleC2×C11×C71C2×C7
LCSG ▷ C71
UCSC1 ◁ C2×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1562

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21868, 15);