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C5×#6400 #11764497

order1120
isoclinismisoclinic class of #6400
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#6400

Splittings

FittingC5×C7×D8 ⋊ C2
HallC5×C7 ⋊ D16
SylowC7 ⋊ C5×D16

Subgroups

subgroupG/H
centerC2×C5#1141
commutator, cosocleC7×C8C22×C5
FrattiniC8C2×C5×D7
FittingC5×C7×D8C2
socleC2×C5×C7D8
hypercenterC5×D8D7
hypocenterC7C5×D16
LCSG ▷ C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×D8

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 560

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 103);