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C5×#6464 #11765059

order1120
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#6464

Splittings

FittingC2×C5×C7×C8 ⋊ C2
HallC5×C7 ⋊ #131
SylowC7 ⋊ C5×#131

Subgroups

subgroupG/H
centerC5×C8C2×D7
commutatorC2×C7C22×C4×C5
FrattiniC4C22×C5×D7
FittingC2×C5×C7×C8C2
socleC2×C5×C7C22×C4
prime radicalC5×#1157C2
cosocleC4×C7C23×C5
hypercenterC2×C5×C8D7
hypocenterC7C5×#131
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C5×C8 ◁ C2×C5×C8

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 665);