Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11677 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#13288 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,16)(17,19)(20,21)(22,32,37,47)(23,38)(24,28)(25,42)(26,31)(27,35,45,40)(29,33)(30,39)(34,44,49,51)(36,43,50,48)(41,46);(13,16)(17,18)(20,22,33,49,39,50,24,40,26,37,23,34,25,36,41,35)(21,27,28,43,42,51,29,47,31,45,46,48,30,44,38,32);(12,14,15,19)(13,17,16,18)(20,23,39,41,26,33,25,24)(21,28,42,29,31,46,30,38)(22,34,50,35,37,49,36,40)(27,43,51,47,45,48,44,32)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6276);