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C11×#23879 #14601072

order2816
nilpotency class3
isoclinismisoclinic class of #23876
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC11×#23879

Subgroups

subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

1840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 352

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

473 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16867);