Finite Group Databasebeta

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C121×C22⋊(C7⋊C9) #44478804

order30492
automorphism?
homologyAbelianization (H1) = C9×C121 · Schur multiplier (H2) = C2

Aliases

direct productC121×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C7⋊C9×C121)
unambiguous semidirect productC7⋊(C22⋊C9×C121)
unambiguous semidirect product(C22×C121)⋊(C7⋊C9)
unambiguous semidirect product(C7×C121)⋊(C22⋊C9)

Splittings

derived, HallC22×C7 ⋊ C9×C121
HallC22×C7×C121 ⋊ C9
HallC7×C121 ⋊ C22⋊C9
HallC22×C121 ⋊ C7⋊C9
SylowC7 ⋊ C22⋊C9×C121
SylowC22 ⋊ C7⋊C9×C121

Subgroups

subgroupG/H
center, hypercenterC3×C121C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C9×C121
FrattiniC3×C11C11×C22⋊ΓL(1,𝔽8)
FittingC22×C3×C7×C121C3
socle, prime radical, cosocleC22×C3×C7×C11C3×C11
LCSG ▷ C22×C7
UCSC1 ◁ C3×C121

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15246

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 27);