Finite Group Databasebeta

← Prev (#14639863) Next (#14639865) →

C22×C11×#538 #14639864

order2816
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C26×C11 · Schur multiplier (H2) = C213

Aliases

direct productC22×C11×#538

Subgroups

subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC22C26×C11
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

9566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 704

A minimal faithful permutation representation — 6 generators on 31 points:

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

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, 55659);