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C22×C9×C71⋊C7 #31822007

order17892
isoclinismisoclinic class of C71⋊C7
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC22×C9×C71⋊C7
unambiguous semidirect product(C22×C9×C71)⋊C7

Splittings

Fitting, HallC22×C9×C71 ⋊ C7
derived, SylowC71 ⋊ C22×C7×C9
HallC9×C71 ⋊ C22×C7
HallC22×C71 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC22×C9C71⋊C7
commutator, hypocenterC71C22×C7×C9
FrattiniC3C22×C3×C71⋊C7
FittingC22×C9×C71C7
socleC22×C3×C71C3×C7
prime radicalC22×C3×C71⋊C7C3
cosocleC3×C71C22×C3×C7
LCSG ▷ C71
UCSC1 ◁ C22×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2556

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 24);