Finite Group Databasebeta

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C5×#68663 #14297470

order1920
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68663

Splittings

FittingC3×C5×#336 ⋊ C2
HallC3×C5 ⋊ #1798
SylowC3 ⋊ C5×#1798

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#336C2
socleC23×C3×C5C22×C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#336D3
hypocenterC3C5×#1798
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C5×#336

624 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)(10,12)(19,25)(22,28)(26,31)(29,32);(7,8)(13,14,15,16)(17,19)(18,22)(20,26)(21,25)(23,29)(24,28)(27,31)(30,32);(9,10)(11,12)(14,16)(17,18,20,23,21,24,27,30)(19,22,26,29,25,28,31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 23168);