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C11×#1144 #11927677

order1232
isoclinismisoclinic class of #1141
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#1144

Splittings

HallC7×C11 ⋊ Q16
SylowC7 ⋊ C11×Q16

Subgroups

subgroupG/H
centerC2×C11C22⋊D7
commutator, cosocleC4×C7C22×C11
FrattiniC4C2×C11×D7
FittingC7×Q8×C11C2
socle, prime radicalC2×C7×C11D4
hypercenterQ8×C11D7
hypocenterC7C11×Q16
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ Q8×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 1232

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17,18,16,14)(19,21,23,29)(20,24,26,33)(22,31,32,28)(25,34,30,27);(13,14)(15,16)(17,18)(19,20,23,26)(21,27,29,34)(22,30,32,25)(24,31,33,28)

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1232, 60);