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C5×#1840⋊C3 #14510688

order1920
isoclinismisoclinic class of #396⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#1840⋊C3
unambiguous semidirect product#1840⋊(C3×C5)
unambiguous semidirect product(C5×#1840)⋊C3

Splittings

Fitting, HallC5×#1840 ⋊ C3
Sylow#1840 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5#126⋊C3
commutator, hypocenter#95C3×C4×C5
FrattiniC22×C4C2×C5×A4
FittingC5×#1840C3
socleC23×C5C4×A4
prime radicalC5×#95⋊C3C4
cosocle#376C2×C3×C5
LCSG ▷ #95
UCSC1 ◁ C4×C5

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2,3,4,5)(6,12,45,13,21,28,23,30,41,7,19,49,11,17,38,15,8,36,9,29,18,16,27,46)(10,33,53,32,42,48,25,31,52,14,20,47,26,44,39,35,24,51,22,37,40,34,43,50);(6,25)(7,32)(8,24)(9,10)(11,22)(12,33)(13,34)(14,15)(16,35)(17,44)(18,38,41,45)(19,20)(21,42)(23,26)(27,43)(28,49,36,46)(29,37)(30,31)(39,40,53,52)(47,48,50,51)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236386);