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C11×#4065 #13183132

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

Aliases

direct productC11×#4065

Splittings

FittingC5×C11×Q16 ⋊ C2
HallC5×C11 ⋊ #135
SylowC5 ⋊ C11×#135

Subgroups

subgroupG/H
centerC2×C11D4×D5
commutator, cosocleC4×C5C23×C11
FrattiniC4C22×D5×C11
FittingC5×C11×Q16C2
socleC2×C5×C11C2×D4
hypercenterC11×Q16D5
hypocenterC5C11×#135
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ C11×Q16

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

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, 941);