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C11×#1204 #13050368

order1320
isoclinismisoclinic class of #1201
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#1204

Splittings

HallC3×C5×C11 ⋊ Q8
HallC5×C11 ⋊ Dic6
HallC3×C11 ⋊ Dic10
HallC3×C5 ⋊ Q8×C11
SylowC5 ⋊ C11×Dic6
SylowC3 ⋊ C11×Dic10

Subgroups

subgroupG/H
center, hypercenterC2×C11D3×D5
commutator, cosocleC2×C3×C5C22×C11
FrattiniC2D3×D5×C11
Fitting, socle, prime radicalC2×C3×C5×C11C22
hypocenterC3×C5Q8×C11
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 1320

A minimal faithful permutation representation — 2 generators on 27 points:

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

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, 72);