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C11×#23912 #14601105

order2816
nilpotency class3
isoclinismisoclinic class of #23912
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC11×#23912

Subgroups

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

1950 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)(16,17)(18,25)(19,23)(20,28)(21,24)(22,26)(27,30)(29,31);(12,13)(14,15)(19,20)(23,28)(25,30)(26,29);(13,15)(16,18)(17,22)(19,26)(20,29)(21,27)(23,30)(24,31)(25,28);(16,19)(17,23)(18,26)(20,21)(22,30)(24,28)(25,31)(27,29)

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16900);