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C11×#36593 #14613786

order2816
nilpotency class2
isoclinismisoclinic class of D4×#120
automorphism?
homologyAbelianization (H1) = C25×C11 · Schur multiplier (H2) = C28

Aliases

direct productC11×#36593

Subgroups

subgroupG/H
center, socle, prime radicalC23×C11C25
commutator, Frattini, cosocleC23C25×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

2162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 2816

A minimal faithful permutation representation — 5 generators on 31 points:

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

Conjugacy classes & character table

770 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 29581);