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C11×#4058 #13183125

order1760
automorphism?
homologyAbelianization (H1) = C23×C11 · Schur multiplier (H2) = C22

Aliases

direct productC11×#4058

Splittings

FittingC5×C11×D8 ⋊ C2
HallC5×C11 ⋊ #135
SylowC5 ⋊ C11×#135

Subgroups

subgroupG/H
centerC2×C11D4×D5
commutator, cosocleC4×C5C23×C11
FrattiniC4C22×D5×C11
FittingC5×C11×D8C2
socleC2×C5×C11C2×D4
hypercenterC11×D8D5
hypocenterC5C11×#135
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ C11×D8

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)(18,23)(19,26)(20,29)(22,30)(25,32)(27,28);(17,19)(18,22)(20,26)(21,28)(23,25)(24,32)(27,29)(30,31);(13,14)(15,16)(17,18)(19,25)(20,24)(21,23)(22,28)(26,30)(27,32)(29,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 934);