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C5×#87640 #14519958

order1960
isoclinismisoclinic class of #87640
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#87640

Splittings

HallC5×C72 ⋊ D4
SylowC72 ⋊ C5×D4

Subgroups

subgroupG/H
center, hypercenterC2×C5D72
commutator, cosocleC2×C72C22×C5
FrattiniC2C5×D72
Fitting, socleC2×C5×C72C22
hypocenterC72C5×D4
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C2×C5

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 280

A minimal faithful permutation representation — 2 generators on 23 points:

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

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 55);