Finite Group Databasebeta

← Prev (#14601105) Next (#14601107) →

C11×#23913 #14601106

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

Aliases

direct productC11×#23913

Subgroups

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

1898 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)(23,27)(25,28)(30,31);(12,13)(14,15)(16,17,20,22)(18,21,25,30)(19,27,26,23)(24,31,28,29);(13,15)(16,18)(17,21)(19,28)(20,25)(22,30)(23,31)(24,26)(27,29);(17,22)(19,26)(21,30)(24,28)

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, 16901);