Finite Group Databasebeta

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C2×C5×C11⋊C5×C19⋊C3 #44535472

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

Aliases

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

Splittings

Fitting, socleC2×C5×C11×C19 ⋊ C3×C5
derived, HallC11×C19 ⋊ C2×C3×C52
HallC2×C5×C19×C11⋊C5 ⋊ C3
HallC5×C19×C11⋊C5 ⋊ C2×C3
HallC2×C11×C19⋊C3 ⋊ C52
HallC11×C19⋊C3 ⋊ C2×C52
HallC2×C11×C19 ⋊ C3×C52
HallC2×C19 ⋊ C3×C5×C11⋊C5
HallC2×C11 ⋊ C52×C19⋊C3
SylowC19 ⋊ C2×C3×C5×C11⋊C5
SylowC11 ⋊ C2×C52×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊C5×C19⋊C3
commutator, cosocle, hypocenterC11×C19C2×C3×C52
FrattiniC1G
Fitting, socleC2×C5×C11×C19C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2090

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 45);