Finite Group Databasebeta

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C137×C22⋊(C7⋊C9) #46828588

order34524
automorphism?
homologyAbelianization (H1) = C9×C137 · Schur multiplier (H2) = C2

Aliases

direct productC137×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C7⋊C9×C137)
unambiguous semidirect productC7⋊(C22⋊C9×C137)
unambiguous semidirect product(C22×C137)⋊(C7⋊C9)
unambiguous semidirect product(C7×C137)⋊(C22⋊C9)

Splittings

derived, HallC22×C7 ⋊ C9×C137
HallC22×C7×C137 ⋊ C9
HallC7×C137 ⋊ C22⋊C9
HallC22×C137 ⋊ C7⋊C9
SylowC7 ⋊ C22⋊C9×C137
SylowC22 ⋊ C7⋊C9×C137

Subgroups

subgroupG/H
center, hypercenterC3×C137C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C9×C137
FrattiniC3C22⋊ΓL(1,𝔽8)×C137
Fitting, socle, prime radicalC22×C3×C7×C137C3
cosocleC22×C3×C7C3×C137
LCSG ▷ C22×C7
UCSC1 ◁ C3×C137

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17262

Conjugacy classes & character table

4932 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 31);