Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42×C11 · Schur multiplier (H2) = C28×C4 |
| direct product | C11×#60058 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C2 | C23×C42×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C24×C4 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
3178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,20,24,21,25,31,37)(18,22,28,34,27,33,40,44)(19,23,30,36,29,35,41,45)(26,32,39,43,38,42,46,47);(12,13,14,15)(16,18)(17,22)(19,26)(20,28)(21,27)(23,32)(24,34)(25,33)(29,38)(30,39)(31,40)(35,42)(36,43)(37,44)(41,46)(45,47);(16,19)(17,23)(18,26)(20,30)(21,29)(22,32)(24,36)(25,35)(27,38)(28,39)(31,41)(33,42)(34,43)(37,45)(40,46)(44,47);(19,29)(23,35)(26,38)(30,41)(32,42)(36,45)(39,46)(43,47);(18,27)(22,33)(26,38)(28,40)(32,42)(34,44)(39,46)(43,47)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53046);