Finite Group Databasebeta

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C11×#4131 #13183337

order1760
automorphism?
homologyAbelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×#4131

Splittings

HallC5×C11 ⋊ #131
SylowC5 ⋊ C11×#131

Subgroups

subgroupG/H
centerC2×C11C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C11
FrattiniC2C22×C11×AGL(1,𝔽5)
FittingC5×D4×C11C4
socleC2×C5×C11C22×C4
prime radicalC11×#711C2
cosocleDic5C23×C11
hypercenterD4×C11AGL(1,𝔽5)
hypocenterC5C11×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ D4×C11

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 880

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1146);