Finite Group Databasebeta

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C5×#67618 #14277188

order1920
isoclinismisoclinic class of #4451
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#67618

Splittings

HallC3×C5 ⋊ #1297
SylowC3 ⋊ C5×#1297

Subgroups

subgroupG/H
centerC2×C4×C5(C2×D3)⋊C4
commutatorC2×C3×C4C42×C5
FrattiniC23×C4C2×C5×D3
FittingC3×C4×C5×C22⋊C4C2
socleC22×C3×C5#95
prime radicalC24×C3×C5D4
cosocleC23×C3×C4C22×C5
hypercenterC4×C5×C22⋊C4D3
hypocenterC3C5×#1297
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C4×C5×C22⋊C4

492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 24 points:

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

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, 2886);