Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C11 · Schur multiplier (H2) = C214 |
| direct product | C11×#62653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C26 |
| commutator | C2 | C25×C4×C11 |
| Frattini, cosocle | C22 | C26×C11 |
| prime radical | C22×C11×2−1+4 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
10930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 6 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,23)(19,24)(20,32)(21,22)(25,33)(26,36)(27,41)(28,34)(29,38)(30,44)(31,35)(37,42)(39,45)(40,47)(43,46);(17,22)(23,34)(24,35)(25,32)(36,38)(37,41)(39,44)(46,47);(16,18,21,28)(17,23,22,34)(19,29,31,26)(20,27,33,42)(24,38,35,36)(25,37,32,41)(30,43,45,40)(39,47,44,46);(16,19,21,31)(17,24,22,35)(18,26,28,29)(20,30,33,45)(23,36,34,38)(25,39,32,44)(27,40,42,43)(37,46,41,47);(16,17)(18,23)(19,24)(20,25)(21,22)(26,36)(27,37)(28,34)(29,38)(30,39)(31,35)(32,33)(40,46)(41,42)(43,47)(44,45);(16,20)(17,25)(18,27)(19,30)(21,33)(22,32)(23,37)(24,39)(26,40)(28,42)(29,43)(31,45)(34,41)(35,44)(36,46)(38,47)1430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55641);