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C5⋊(C5⋊(C11⋊(D19⋊C3))) #44535515

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

Aliases

unambiguous semidirect productC5⋊(C5⋊(C11⋊(D19⋊C3)))
unambiguous semidirect productC11⋊(C5⋊(C5⋊(D19⋊C3)))
unambiguous semidirect product(C19⋊C3)⋊(C5⋊D55)

Splittings

Fitting, socle, derived, HallC52×C11×C19 ⋊ C2×C3
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, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C11×C19C2×C3
LCSG ▷ C52×C11×C19
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 5225

A minimal faithful permutation representation — 3 generators on 40 points:

(2,3)(4,5)(7,8)(9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(23,27,28,24,25,29)(26,35,32,30,31,37)(33,38,40,39,36,34);(6,7,9,10,8)(11,12,14,16,18,20,21,19,17,15,13)(22,23,26,32,38,35,39,25,29,34,40,28,27,33,31,36,37,30,24);(1,2,4,5,3)

Polycyclic presentation:

2,3,5^2,11,19|c^a=c^4,d^a=d^4,e^a=e^10,f^a=f^18,f^b=f^7

Conjugacy classes & character table

1242 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 88);