Finite Group Databasebeta

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C5×#67731 #14278918

order1920
isoclinismisoclinic class of #4487
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#67731

Splittings

HallC3×C5 ⋊ #1385
SylowC3 ⋊ C5×#1385

Subgroups

subgroupG/H
centerC4×C5#808
commutatorC3×C8C42×C5
FrattiniC22×C8C2×C5×D3
FittingC2×C3×C5×#108C2
socleC2×C3×C5#340
prime radicalC23×C3×C5Q16
cosocleC22×C3×C8C22×C5
hypercenterC2×C5×#108D3
hypocenterC3C5×#1385
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C22×C5×C8 ◁ C2×C5×#108

248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(7,8)(9,11,14,25,13,29,28,40,16,26,27,39,15,24,12,23)(10,17,20,33,31,32,18,22,21,35,36,37,19,34,30,38);(6,7,8)(9,10,13,19,16,21,15,31)(11,22,24,37,26,38,29,33)(12,20,14,30,28,36,27,18)(17,25,32,23,35,39,34,40)

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4616);