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C7×#4047 #11765145

order1120
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22

Aliases

direct productC7×#4047

Splittings

FittingC2×C5×C7×C8 ⋊ C2
HallC5×C7 ⋊ #131
SylowC5 ⋊ C7×#131

Subgroups

subgroupG/H
centerC7×C8C2×D5
commutatorC2×C5C22×C4×C7
FrattiniC4C22×C7×D5
FittingC2×C5×C7×C8C2
socleC2×C5×C7C22×C4
prime radicalC7×#709C2
cosocleC4×C5C23×C7
hypercenterC2×C7×C8D5
hypocenterC5C7×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C7×C8 ◁ C2×C7×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)(8,9,11,12,10)(13,15,16,21,17,22,23,27)(14,19,20,26,18,24,25,28);(14,18)(19,24)(20,25)(26,28);(9,10)(11,12)(13,14)(15,19)(16,20)(17,18)(21,26)(22,24)(23,25)(27,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 751);