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A5×#87704 #37561655

order23940
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C2

Aliases

direct productA5×#87704

Splittings

Fitting, HallC7×C19 ⋊ C3×A5
socle, derivedC7×C19×A5 ⋊ C3
SylowC19 ⋊ ΓL(1,𝔽8)×A5
SylowC7 ⋊ C19⋊C3×A5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, socle, hypocenterC7×C19×A5C3
Fitting, cosocleC7×C19C3×A5
LCSG ▷ C7×C19×A5
UCSC1

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 665

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,4)(3,5,6)(8,12,21)(9,14,25)(10,18,11)(13,23,17)(15,22,24)(16,26,20)(27,28,29,30,31);(1,4,3)(2,5,7)(8,9,11)(10,13,17)(12,15,20)(14,19,21)(16,22,18)(23,25,26)(27,30,28,29,31)

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 787);