Finite Group Databasebeta

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C2×C3×C5×C19×C11⋊C5 #44535517

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C19 · Schur multiplier (H2) = C5

Aliases

direct productC2×C3×C5×C19×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C3×C52×C19)
unambiguous semidirect product(C2×C3×C11)⋊(C52×C19)
unambiguous semidirect product(C2×C5×C11)⋊(C3×C5×C19)
unambiguous semidirect product(C2×C3×C5×C11)⋊(C5×C19)
unambiguous semidirect product(C2×C3×C11×C19)⋊C52
unambiguous semidirect product(C2×C3×C5×C11×C19)⋊C5

Splittings

Fitting, socleC2×C3×C5×C11×C19 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C52×C19
HallC2×C3×C11×C19 ⋊ C52
HallC3×C11×C19 ⋊ C2×C52
HallC2×C11×C19 ⋊ C3×C52
HallC11×C19 ⋊ C2×C3×C52
HallC2×C3×C11 ⋊ C52×C19
HallC3×C11 ⋊ C2×C52×C19
HallC2×C11 ⋊ C3×C52×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C19C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C52×C19
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C19C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C19

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6270

Conjugacy classes & character table

3990 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 90);