Finite Group Databasebeta

← Prev (#14600594) Next (#14600596) →

C11×#23402 #14600595

order2816
nilpotency class3
isoclinismisoclinic class of #23400
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C27

Aliases

direct productC11×#23402

Subgroups

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

2198 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)(12,13)(14,15)(16,17)(18,25)(19,23)(20,28)(21,24)(22,26)(27,31)(29,30);(16,18)(17,22)(19,26)(20,29)(21,27)(23,31)(24,30)(25,28);(13,15)(19,20)(22,30)(23,28)(26,29);(16,19,21,20)(17,23,24,28)(18,26,27,29)(22,31,30,25)

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, 16390);