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C11×#4050 #13183117

order1760
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×#4050

Splittings

FittingC2×C5×C8×C11 ⋊ C2
HallC5×C11 ⋊ #135
SylowC5 ⋊ C11×#135

Subgroups

subgroupG/H
centerC4×C11D20
commutator, cosocleC4×C5C23×C11
FrattiniC4C22×D5×C11
FittingC2×C5×C8×C11C2
socleC2×C5×C11C2×D4
hypercenterC2×C8×C11D5
hypocenterC5C11×#135
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C11 ◁ C2×C4×C11 ◁ C2×C8×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)(12,13,15,16,14)(17,20,21,28,22,29,19,26)(18,24,23,27,25,31,30,32);(17,19,22,21)(18,23,25,30)(20,26,29,28)(24,27,31,32);(13,14)(15,16)(17,18)(19,23)(20,27)(21,30)(22,25)(24,28)(26,31)(29,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 926);