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C49×C22⋊(C13⋊C9) #37524121

order22932
automorphism?
homologyAbelianization (H1) = C9×C49 · Schur multiplier (H2) = C2

Aliases

direct productC49×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C49×C13⋊C9)
unambiguous semidirect productC13⋊(C22⋊C9×C49)

Splittings

derived, HallC22×C13 ⋊ C9×C49
HallC22×C13×C49 ⋊ C9
HallC13×C49 ⋊ C22⋊C9
HallC22×C49 ⋊ C13⋊C9
SylowC13 ⋊ C22⋊C9×C49
SylowC22 ⋊ C49×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C49C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C9×C49
FrattiniC3×C7C7×C22⋊(C13⋊C3)
FittingC22×C3×C13×C49C3
socle, prime radical, cosocleC22×C3×C7×C13C3×C7
LCSG ▷ C22×C13
UCSC1 ◁ C3×C49

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11466

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 66);