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C7×#4020 #11765118

order1120
automorphism?
homologyAbelianization (H1) = C23×C7 · Schur multiplier (H2) = C22×C4

Aliases

direct productC7×#4020

Splittings

FittingC42×C5×C7 ⋊ C2
HallC5×C7 ⋊ #127
SylowC5 ⋊ C7×#127

Subgroups

subgroupG/H
centerC22×C7C22×D5
commutator, cosocleC22×C5C23×C7
FrattiniC22C22×C7×D5
FittingC42×C5×C7C2
socleC22×C5×C7C23
hypercenterC42×C7D5
hypocenterC5C7×#127
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C7 ◁ C42×C7

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 560

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 724);