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C2×C11×#2543 #14612011

order2816
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C25×C11 · Schur multiplier (H2) = C29

Aliases

direct productC2×C11×#2543

Subgroups

subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

4326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 1408

A minimal faithful permutation representation — 5 generators on 29 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29);(4,6)(11,12)(13,17)(14,15)(16,18);(7,8,9,10)(12,15)(16,17);(3,4,5,6)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18);(11,13)(12,16)(14,18)(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, 27806);