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C11⋊(C25⋊(D19⋊C3)) #44535460

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

Aliases

unambiguous semidirect productC11⋊(C25⋊(D19⋊C3))
unambiguous semidirect productC25⋊(C11⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊D275
unambiguous semidirect productD5225⋊C3

Splittings

Fitting, derived, HallC11×C19×C25 ⋊ C2×C3
HallC11×C25×C19⋊C3 ⋊ C2
HallD5225 ⋊ C3
HallC25×C19⋊C3 ⋊ D11
HallC11×C19⋊C3 ⋊ D25
HallC19×C25 ⋊ C3×D11
HallC11×C25 ⋊ D19⋊C3
HallC11×C19 ⋊ C3×D25
HallC19⋊C3 ⋊ D275
SylowC25 ⋊ C11⋊(D19⋊C3)
SylowC19 ⋊ C3×D275
SylowC11 ⋊ C25⋊(D19⋊C3)

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC11×C19×C25C2×C3
FrattiniC5C5⋊(C11⋊(D19⋊C3))
socleC5×C11×C19C3×D5
LCSG ▷ C11×C19×C25
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 5225

A minimal faithful permutation representation — 2 generators on 55 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,17,18,14,15,19)(16,25,22,20,21,27)(23,28,30,29,26,24)(32,34)(33,37)(35,40)(36,43)(38,46)(39,45)(41,42)(44,50)(47,51)(48,52)(49,54)(53,55);(1,2,4,6,8,10,11,9,7,5,3)(12,13,16,22,28,25,29,15,19,24,30,18,17,23,21,26,27,20,14)(31,45,55,48,34,37,51,49,40,43,46,44,42,41,50,38,36,35,54,47,33,32,52,53,39)

Polycyclic presentation:

2,3,5,11,19,5|c^5=f^4,c^a=c^4f,d^a=d^10,e^a=e^18,f^a=f^4,e^b=e^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, 33);