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C71×C22⋊(C7⋊C9) #31822020

order17892
isoclinismisoclinic class of C22⋊ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C9×C71 · Schur multiplier (H2) = C2

Aliases

direct productC71×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C7⋊C9×C71)
unambiguous semidirect productC7⋊(C22⋊C9×C71)
unambiguous semidirect product(C22×C71)⋊(C7⋊C9)
unambiguous semidirect product(C7×C71)⋊(C22⋊C9)

Splittings

derived, HallC22×C7 ⋊ C9×C71
HallC22×C7×C71 ⋊ C9
HallC7×C71 ⋊ C22⋊C9
HallC22×C71 ⋊ C7⋊C9
SylowC7 ⋊ C22⋊C9×C71
SylowC22 ⋊ C7⋊C9×C71

Subgroups

subgroupG/H
center, hypercenterC3×C71C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C9×C71
FrattiniC3C71×C22⋊ΓL(1,𝔽8)
Fitting, socle, prime radicalC22×C3×C7×C71C3
cosocleC22×C3×C7C3×C71
LCSG ▷ C22×C7
UCSC1 ◁ C3×C71

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8946

Conjugacy classes & character table

2556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 37);