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C11×#1201 #13050365

order1320
isoclinismisoclinic class of #1201
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#1201

Splittings

HallC3×C5×C11 ⋊ D4
HallC5×C11 ⋊ #67
HallC3×C11 ⋊ C22⋊D5
HallC3×C5 ⋊ D4×C11
SylowC5 ⋊ C11×#67
SylowC3 ⋊ C11×C22⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C11D3×D5
commutator, cosocleC2×C3×C5C22×C11
FrattiniC2D3×D5×C11
Fitting, socleC2×C3×C5×C11C22
hypocenterC3×C5D4×C11
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 660

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(18,19)(21,23);(13,14)(15,16)(17,18,19)(20,21)(22,23)

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 69);