Finite Group Databasebeta

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C5×#70745 #14285541

order1920
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#70745

Splittings

HallC3×C5 ⋊ #1564
SylowC3 ⋊ C5×#1564

Subgroups

subgroupG/H
centerC42×C5#67
commutatorC3×C4C22×C5×C8
FrattiniC42C22×C5×D3
FittingC3×C5×#431C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×C5C4⋊C4
cosocleC3×C42C23×C5
hypercenterC5×#431D3
hypocenterC3C5×#1564
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C42×C5 ◁ C2×C42×C5 ◁ C5×#431

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 11239);