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A5×#87705 #37561656

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

Aliases

direct productA5×#87705

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

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, 788);