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C11×#4133 #13183339

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

Aliases

direct productC11×#4133

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×Q8×C11C4
socleC2×C5×C11C22×C4
prime radicalC11×#713C2
cosocleDic5C23×C11
hypercenterQ8×C11AGL(1,𝔽5)
hypocenterC5C11×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ Q8×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)(17,20,22,21)(18,24,26,25)(19,27,28,29)(23,30,31,32);(17,19,22,28)(18,23,26,31)(20,29,21,27)(24,32,25,30);(13,14,15,16)(17,18,21,25,22,26,20,24)(19,23,27,30,28,31,29,32)

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, 1148);