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C11⋊C5×C22⋊#4294 #49178342

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

Aliases

direct productC11⋊C5×C22⋊#4294
unambiguous semidirect productC22⋊(C11⋊C5×#4294)
unambiguous semidirect productC11⋊(C5×C22⋊#4294)
unambiguous semidirect product(C22×C11⋊C5)⋊#4294
unambiguous semidirect product(C11×C22⋊#4294)⋊C5

Splittings

derived, HallC22×C11×C19 ⋊ C5×C9
HallC11×C22⋊#4294 ⋊ C5
HallC22×C19×C11⋊C5 ⋊ C9
HallC19×C11⋊C5 ⋊ C22⋊C9
HallC22×C11⋊C5 ⋊ #4294
HallC11×C19 ⋊ C5×C22⋊C9
HallC22×C19 ⋊ C9×C11⋊C5
HallC22×C11 ⋊ C5×#4294
SylowC19 ⋊ C22⋊C9×C11⋊C5
SylowC11 ⋊ C5×C22⋊#4294
SylowC22 ⋊ C11⋊C5×#4294

Subgroups

subgroupG/H
center, Frattini, hypercenterC3C11⋊C5×C22⋊(C19⋊C3)
commutator, hypocenterC22×C11×C19C5×C9
Fitting, socle, cosocleC22×C3×C11×C19C3×C5
prime radicalC22×C3×C19×C11⋊C5C3
LCSG ▷ C22×C11×C19
UCSC1 ◁ C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3762

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 51);