Finite Group Databasebeta

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C2×C11×#2018 #14600628

order2816
nilpotency class3
isoclinismisoclinic class of #2018
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC2×C11×#2018

Subgroups

subgroupG/H
center, socleC23×C11#121
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

2158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 704

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16423);