Finite Group Databasebeta

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C2×C11×#2330 #14611265

order2816
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C28

Aliases

direct productC2×C11×#2330

Subgroups

subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

2398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 2816

A minimal faithful permutation representation — 5 generators on 33 points:

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

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 27060);