Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11×C16 · Schur multiplier (H2) = C25 |
| direct product | C11×#33496 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C2 | C23×C11×C16 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C23×C8 |
| prime radical | C23×C11 | C22×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
526 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,26)(23,25)(24,27)(28,29,30,33,31,34,36,39,32,35,37,40,38,41,42,43);(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25);(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26);(13,19)(17,20)(18,27)(25,26)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26484);