Finite Group Databasebeta

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C11×C5⋊(C5⋊(D19⋊C3)) #44535513

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×C5⋊(C5⋊(D19⋊C3))
unambiguous semidirect productC5⋊(C11×C5⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C11×C5⋊D5)

Splittings

Fitting, socle, HallC52×C11×C19 ⋊ C2×C3
derived, HallC52×C19 ⋊ C2×C3×C11
HallC52×C11×C19⋊C3 ⋊ C2
HallC11×C5⋊D95 ⋊ C3
HallC52×C19⋊C3 ⋊ C2×C11
HallC5⋊D95 ⋊ C3×C11
HallC11×C19⋊C3 ⋊ C5⋊D5
HallC52×C11 ⋊ D19⋊C3
HallC11×C19 ⋊ C3×C5⋊D5
HallC19⋊C3 ⋊ C11×C5⋊D5
SylowC52 ⋊ C11×D19⋊C3
SylowC19 ⋊ C3×C11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC11C5⋊(C5⋊(D19⋊C3))
commutator, cosocle, hypocenterC52×C19C2×C3×C11
FrattiniC1G
Fitting, socleC52×C11×C19C2×C3
LCSG ▷ C52×C19
UCSC1 ◁ C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 86);