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C11×#23908 #14601101

order2816
nilpotency class3
isoclinismisoclinic class of #23906
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC11×#23908

Subgroups

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

1814 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)(18,24)(19,26)(21,29)(22,27)(25,28)(30,31);(12,13)(14,15)(16,17,20,23)(18,21,25,30)(19,27,26,22)(24,31,28,29);(13,15)(16,18)(17,21)(19,28)(20,25)(22,31)(23,30)(24,26)(27,29);(19,26)(22,27)(24,28)(29,31)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16896);