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C19⋊C3×PSL(2,𝔽11) #49178797

order37620
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C2

Aliases

direct productC19⋊C3×PSL(2,𝔽11)
unambiguous semidirect productC19⋊(C3×PSL(2,𝔽11))
unambiguous semidirect product(C19×PSL(2,𝔽11))⋊C3

Splittings

Fitting, SylowC19 ⋊ C3×PSL(2,𝔽11)
socle, derivedC19×PSL(2,𝔽11) ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, socle, hypocenterC19×PSL(2,𝔽11)C3
Fitting, cosocleC19C3×PSL(2,𝔽11)
LCSG ▷ C19×PSL(2,𝔽11)
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 209

A minimal faithful permutation representation — 2 generators on 30 points:

(1,4,9,10,6,11,7,2,5,8,3)(12,24,16)(13,29,19)(14,15,22)(17,26,25)(18,21,28)(20,23,30);(1,7,11,10,2)(3,8,9,6,4)(12,14,29)(13,20,27)(15,17,30)(16,21,22)(18,19,23)(25,28,26)

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 506);