Finite Group Databasebeta

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C5×#67680 #14277204

order1920
isoclinismisoclinic class of #4451
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#67680

Splittings

HallC3×C5 ⋊ #1298
SylowC3 ⋊ C5×#1298

Subgroups

subgroupG/H
centerC2×C4×C5(C2×D3)⋊C4
commutatorC2×C3×C4C42×C5
FrattiniC23×C4C2×C5×D3
FittingC2×C3×C5×C22⋊C8C2
socleC22×C3×C5#95
prime radicalC24×C3×C5Q8
cosocleC23×C3×C4C22×C5
hypercenterC2×C5×C22⋊C8D3
hypocenterC3C5×#1298
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C2×C5×C22⋊C8

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2902);