Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
496 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(20,21,26,31)(22,27,34,43)(23,35,37,46)(24,30,25,29)(28,39,45,38)(32,44,48,51)(33,47,40,42)(36,41,49,50);(12,13,16,18)(14,17,15,19)(20,22)(21,27)(23,36)(24,33)(25,40)(26,34)(28,44)(29,42)(30,47)(31,43)(32,39)(35,50)(37,49)(38,48)(41,46)(45,51);(12,14,16,15)(13,17,18,19)(20,23)(21,28)(22,32)(24,39)(25,38)(26,37)(27,41)(29,46)(30,35)(31,45)(33,49)(34,48)(36,40)(42,51)(43,50)(44,47)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3175);