Finite Group Databasebeta

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C5×#67754 #14277073

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

Aliases

direct productC5×#67754

Splittings

HallC3×C5 ⋊ #1291
SylowC3 ⋊ C5×#1291

Subgroups

subgroupG/H
centerC22×C5C3⋊#95
commutatorC2×C3×C4C42×C5
FrattiniC2×C42C2×C5×D3
FittingC3×C5×#432C2
socleC22×C3×C5#95
prime radicalC23×C3×C5C4⋊C4
cosocleC2×C3×C42C22×C5
hypercenterC5×#432D3
hypocenterC3C5×#1291
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C5×#432

276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

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

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

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, 2771);