Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24 |
| direct product | C2×C11×#1305 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #95 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(3,4,5,8,6,7,9,10)(11,12)(13,17)(14,16)(15,18);(4,7)(5,9)(11,13)(12,15,16,17)(14,18)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1091);