Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#22281 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#3150 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,18)(16,19)(20,21,25,29,26,30,24,39)(22,27,33,41,34,42,32,48)(23,35,38,43,36,49,37,28)(31,44,47,50,45,51,46,40);(12,14,17,13)(15,18,16,19)(20,22,25,33,26,34,24,32)(21,27,29,41,30,42,39,48)(23,31,38,47,36,45,37,46)(28,40,35,44,43,50,49,51);(12,15,17,16)(13,18,14,19)(20,23,24,37,26,36,25,38)(21,28,29,35,30,43,39,49)(22,31,32,46,34,45,33,47)(27,40,41,44,42,50,48,51);(12,16,17,15)(13,18,14,19)(23,36)(28,43)(31,45)(35,49)(37,38)(40,50)(44,51)(46,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15269);