Finite Group Databasebeta

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C5×#68607 #14298936

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC5×#68607

Splittings

HallC3×C5 ⋊ #1839
SylowC3 ⋊ C5×#1839

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC22×C3C22×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#336C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#336D3
hypocenterC3C5×#1839
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C5×#336

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

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

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

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, 24634);