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C11×#4036 #13183104

order1760
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#4036

Splittings

HallC5×C11 ⋊ #125
SylowC5 ⋊ C11×#125

Subgroups

subgroupG/H
centerC22×C11C22×D5
commutator, cosocleC22×C5C23×C11
FrattiniC22C22×D5×C11
FittingC5×C11×C4⋊C4C2
socle, prime radicalC22×C5×C11C23
hypercenterC11×C4⋊C4D5
hypocenterC5C11×#125
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C11×C4⋊C4

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1760

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(18,22)(19,23)(25,27,28,32)(26,29,30,31);(17,19,20,23)(18,21,22,24);(13,14)(15,16)(17,18)(19,21)(20,22)(23,24)(25,26,28,30)(27,31,32,29)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 913);