Finite Group Databasebeta

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C5×C11×C22⋊#4294 #49178412

order37620
automorphism?
homologyAbelianization (H1) = C5×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×C22⋊#4294
unambiguous semidirect productC22⋊(C5×C11×#4294)
unambiguous semidirect product(C22×C5)⋊(C11×#4294)
unambiguous semidirect product(C22×C5×C11)⋊#4294

Splittings

derived, HallC22×C19 ⋊ C5×C9×C11
HallC22×C5×C11×C19 ⋊ C9
HallC5×C11×C19 ⋊ C22⋊C9
HallC22×C11×C19 ⋊ C5×C9
HallC22×C5×C19 ⋊ C9×C11
HallC22×C5×C11 ⋊ #4294
HallC11×C19 ⋊ C5×C22⋊C9
HallC5×C19 ⋊ C11×C22⋊C9
HallC22×C11 ⋊ C5×#4294
HallC22×C5 ⋊ C11×#4294
SylowC19 ⋊ C5×C11×C22⋊C9
SylowC22 ⋊ C5×C11×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C5×C9×C11
FrattiniC3C5×C11×C22⋊(C19⋊C3)
Fitting, socle, prime radicalC22×C3×C5×C11×C19C3
cosocleC22×C3×C19C3×C5×C11
LCSG ▷ C22×C19
UCSC1 ◁ C3×C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18810

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 121);