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C11⋊(C11⋊(D19⋊C3)) #28352256

order13794
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C11

Aliases

unambiguous semidirect productC11⋊(C11⋊(D19⋊C3))
unambiguous semidirect product(C19⋊C3)⋊(C11⋊D11)

Splittings

Fitting, socle, derived, HallC112×C19 ⋊ C2×C3
HallC112×C19⋊C3 ⋊ C2
HallC11⋊D209 ⋊ C3
SylowC112 ⋊ D19⋊C3
HallC19⋊C3 ⋊ C11⋊D11
SylowC19 ⋊ C3×C11⋊D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC112×C19C2×C3
LCSG ▷ C112×C19
UCSC1

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 2299

A minimal faithful permutation representation — 3 generators on 41 points:

(2,6,7,3,4,8)(5,14,11,9,10,16)(12,17,19,18,15,13)(21,22)(23,24)(25,26)(27,28)(29,30)(32,33)(34,35)(36,37)(38,39)(40,41);(1,2,5,11,17,14,18,4,8,13,19,7,6,12,10,15,16,9,3)(31,32,34,36,38,40,41,39,37,35,33);(20,21,23,25,27,29,30,28,26,24,22)

Polycyclic presentation:

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

Conjugacy classes & character table

549 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×C11⋊(D19⋊C3), D19⋊C3×C11⋊D11, C2×C11⋊(C11⋊(D19⋊C3))
maximal normal subgroup ofD11×C11⋊(D19⋊C3), D19⋊C3×C11⋊D11, C2×C11⋊(C11⋊(D19⋊C3))
maximal quotient ofC11⋊(C11⋊((C19⋊C3)⋊C4)), C2×C11⋊(C11⋊(D19⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13794, 17);