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C22×C11×#560 #14639880

order2816
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C26×C11 · Schur multiplier (H2) = C213

Aliases

direct productC22×C11×#560

Subgroups

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

9606 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)(7,14)(8,13)(9,11)(10,16)(12,18)(15,19)(17,20);(5,7)(6,10)(8,16)(9,17)(11,19)(12,20)(13,14)(15,18);(6,11)(7,15)(10,14)(12,13)(16,17)(19,20);(6,12)(7,16)(10,19)(11,13)(14,20)(15,17)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55675);