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C17⋊(C19⋊AGL(1,𝔽11)) #48001059

order35530
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC17⋊(C19⋊AGL(1,𝔽11))
unambiguous semidirect productC19⋊(C17⋊AGL(1,𝔽11))
unambiguous semidirect product(C11⋊C5)⋊D323
unambiguous semidirect productD3553⋊C5

Splittings

Fitting, socle, derived, HallC11×C17×C19 ⋊ C2×C5
HallC17×C19×C11⋊C5 ⋊ C2
HallD3553 ⋊ C5
HallC19×C11⋊C5 ⋊ D17
HallC17×C11⋊C5 ⋊ D19
HallC17×C19 ⋊ AGL(1,𝔽11)
HallC11×C19 ⋊ C5×D17
HallC11×C17 ⋊ C5×D19
HallC11⋊C5 ⋊ D323
SylowC19 ⋊ C17⋊AGL(1,𝔽11)
SylowC17 ⋊ C19⋊AGL(1,𝔽11)
SylowC11 ⋊ C5×D323

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C17×C19C2×C5
LCSG ▷ C11×C17×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 3553

A minimal faithful permutation representation — 2 generators on 47 points:

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

Polycyclic presentation:

2,5,11,17,19|c^a=c^10,d^a=d^16,e^a=e^18,c^b=c^4

Conjugacy classes & character table

1138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 24);