Finite Group Databasebeta

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C5×#68690 #14308872

order1920
isoclinismisoclinic class of #68629
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68690

Splittings

HallC3×C5 ⋊ #2026
SylowC3 ⋊ C5×#2026

Subgroups

subgroupG/H
centerC23×C5C2×D12
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#336C2
socle, prime radicalC23×C3×C5C2×D4
hypercenterC5×#336D3
hypocenterC3C5×#2026
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C5×#336

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 36 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 34570);