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C5×#71860 #14313458

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71860

Splittings

HallC3×C5 ⋊ #2127
SylowC3 ⋊ C5×#2127

Subgroups

subgroupG/H
centerC2×C5C2×#834
commutatorC2×C3×C4C22×C4×C5
FrattiniC2×D4C22×C5×D3
Fitting, prime radicalC3×C5×#535C2
socleC2×C3×C5C2×#99
cosocleC2×C3×D4C23×C5
hypercenterC5×#535D3
hypocenterC3C5×#2127
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C23×C5 ◁ C22×C5×D4 ◁ C5×#535

572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7,8)(11,18)(14,23)(17,24)(19,21);(9,11)(10,14)(12,21)(13,18)(15,24)(16,23)(17,20)(19,22);(7,8)(9,10)(11,17,18,24)(12,20,22,15)(13,16)(14,19)(21,23)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39156);