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C5×#73290 #14511014

order1920
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2×C42

Aliases

direct productC5×#73290

Splittings

Fitting, HallC5×#2811 ⋊ C3
derived, Sylow#2811 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5#5464
commutator, cosocle, hypocenter#2811C3×C5
FrattiniC23C5×C22⋊A4
FittingC5×#2811C3
socleC23×C5C22⋊A4
LCSG ▷ #2811
UCSC1 ◁ C2×C5

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236712);