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C2×C11×#2008 #14600603

order2816
nilpotency class3
isoclinismisoclinic class of #2008
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC2×C11×#2008

Subgroups

subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 352

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16398);