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C5×#87642 #14519960

order1960
isoclinismisoclinic class of #87640
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#87642

Splittings

HallC5×C72 ⋊ Q8
SylowC72 ⋊ C5×Q8

Subgroups

subgroupG/H
center, hypercenterC2×C5D72
commutator, cosocleC2×C72C22×C5
FrattiniC2C5×D72
Fitting, socle, prime radicalC2×C5×C72C22
hypocenterC72C5×Q8
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C2×C5

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 280

A minimal faithful permutation representation — 2 generators on 27 points:

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

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, 57);