Finite Group Databasebeta

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C5×#71905 #14308938

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#71905

Splittings

HallC3×C5 ⋊ #2028
SylowC3 ⋊ C5×#2028

Subgroups

subgroupG/H
centerC22×C5#953
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#544C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenterC5×#544D3
hypocenterC3C5×#2028
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#544

492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 34636);