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D11×C19⋊(C52⋊C3) #44535492

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

Aliases

direct productD11×C19⋊(C52⋊C3)
unambiguous semidirect productC11⋊(C2×C19⋊(C52⋊C3))
unambiguous semidirect product(C19×D11)⋊(C52⋊C3)
unambiguous semidirect product(C52×D11)⋊(C19⋊C3)

Splittings

Fitting, socle, derived, HallC52×C11×C19 ⋊ C2×C3
HallC11×C19⋊(C52⋊C3) ⋊ C2
HallC52×C19×D11 ⋊ C3
HallC52×D11 ⋊ C19⋊C3
HallC52×C19 ⋊ C3×D11
HallC19×D11 ⋊ C52⋊C3
HallC52×C11 ⋊ C2×C19⋊C3
HallC11×C19 ⋊ C2×C52⋊C3
SylowC52 ⋊ D11×C19⋊C3
SylowC19 ⋊ D11×C52⋊C3
SylowC11 ⋊ C2×C19⋊(C52⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C11×C19C2×C3
LCSG ▷ C52×C11×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1127 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 65);