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C4×C9×C19×C11⋊C5 #49178293

order37620
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C19 · Schur multiplier (H2) = C1

Aliases

direct productC4×C9×C19×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C9×C19)
unambiguous semidirect product(C4×C9×C11)⋊(C5×C19)
unambiguous semidirect product(C4×C9×C11×C19)⋊C5

Splittings

Fitting, HallC4×C9×C11×C19 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C9×C19
HallC9×C11×C19 ⋊ C4×C5
HallC4×C11×C19 ⋊ C5×C9
HallC4×C9×C11 ⋊ C5×C19
HallC11×C19 ⋊ C4×C5×C9
HallC9×C11 ⋊ C4×C5×C19
HallC4×C11 ⋊ C5×C9×C19

Subgroups

subgroupG/H
center, hypercenterC4×C9×C19C11⋊C5
commutator, hypocenterC11C4×C5×C9×C19
FrattiniC2×C3C2×C3×C19×C11⋊C5
FittingC4×C9×C11×C19C5
socleC2×C3×C11×C19C2×C3×C5
prime radicalC2×C3×C19×C11⋊C5C2×C3
cosocleC2×C3×C11C2×C3×C5×C19
LCSG ▷ C11
UCSC1 ◁ C4×C9×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7524

Conjugacy classes & character table

4788 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 2);