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C5×#6453 #11765048

order1120
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#6453

Splittings

HallC5×C7 ⋊ #125
SylowC7 ⋊ C5×#125

Subgroups

subgroupG/H
centerC22×C5C22×D7
commutator, cosocleC22×C7C23×C5
FrattiniC22C22×C5×D7
FittingC5×C7×C4⋊C4C2
socle, prime radicalC22×C5×C7C23
hypercenterC5×C4⋊C4D7
hypocenterC7C5×#125
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C5 ◁ C5×C4⋊C4

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1120

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

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

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 654);