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C5×C5⋊(C11⋊(D19⋊C3)) #44535511

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C5⋊(C11⋊(D19⋊C3))
unambiguous semidirect productC5⋊(C5×C11⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C5×D55)
unambiguous semidirect product(C5×D1045)⋊C3

Splittings

Fitting, socle, HallC52×C11×C19 ⋊ C2×C3
derivedC5×C11×C19 ⋊ C2×C3×C5
HallC52×C11×C19⋊C3 ⋊ C2
HallC5×D1045 ⋊ C3
HallC52×C19⋊C3 ⋊ D11
HallC11×C19⋊C3 ⋊ C5×D5
HallC52×C19 ⋊ C3×D11
HallC52×C11 ⋊ D19⋊C3
HallC11×C19 ⋊ C3×C5×D5
HallC19⋊C3 ⋊ C5×D55
SylowC52 ⋊ C11⋊(D19⋊C3)
SylowC19 ⋊ C3×C5×D55
SylowC11 ⋊ C5×C5⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C5⋊(C11⋊(D19⋊C3))
commutator, cosocle, hypocenterC5×C11×C19C2×C3×C5
FrattiniC1G
Fitting, socleC52×C11×C19C2×C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2090

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 84);