Finite Group Databasebeta

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C4×C11⋊C5×#4294 #49178295

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

Aliases

direct productC4×C11⋊C5×#4294
unambiguous semidirect product(C4×C11)⋊(C5×#4294)
unambiguous semidirect product(C4×C11×#4294)⋊C5

Splittings

derived, HallC11×C19 ⋊ C4×C5×C9
HallC4×C11×#4294 ⋊ C5
HallC4×C19×C11⋊C5 ⋊ C9
HallC11×#4294 ⋊ C4×C5
HallC19×C11⋊C5 ⋊ C4×C9
HallC4×C11×C19 ⋊ C5×C9
HallC4×C19 ⋊ C9×C11⋊C5
HallC4×C11 ⋊ C5×#4294
SylowC19 ⋊ C4×C9×C11⋊C5
SylowC11 ⋊ C4×C5×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C4C11⋊C5×C19⋊C3
commutator, hypocenterC11×C19C4×C5×C9
FrattiniC2×C3C2×C11⋊C5×C19⋊C3
FittingC3×C4×C11×C19C3×C5
socle, cosocleC2×C3×C11×C19C2×C3×C5
prime radicalC2×C3×C19×C11⋊C5C2×C3
LCSG ▷ C11×C19
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7524

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 4);