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C43×C22⋊(C7⋊C9) #24925478

order10836
isoclinismisoclinic class of C22⋊ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C9×C43 · Schur multiplier (H2) = C2

Aliases

direct productC43×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C43×C7⋊C9)
unambiguous semidirect productC7⋊(C22⋊C9×C43)

Splittings

derived, HallC22×C7 ⋊ C9×C43
HallC22×C7×C43 ⋊ C9
HallC7×C43 ⋊ C22⋊C9
HallC22×C43 ⋊ C7⋊C9
SylowC7 ⋊ C22⋊C9×C43
SylowC22 ⋊ C43×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C43C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C9×C43
FrattiniC3C43×C22⋊ΓL(1,𝔽8)
Fitting, socle, prime radicalC22×C3×C7×C43C3
cosocleC22×C3×C7C3×C43
LCSG ▷ C22×C7
UCSC1 ◁ C3×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1548 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 70);