Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11236 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #394 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,28)(19,32)(20,26)(21,25)(22,27)(23,30)(24,34)(29,39)(31,42)(33,41)(35,40)(36,38)(37,45)(43,44)(46,47);(16,18,20,30,22,31,21,36)(17,23,25,28,27,38,26,42)(19,29,33,44,35,45,34,46)(24,39,40,47,41,37,32,43);(16,19,20,33,22,35,21,34)(17,24,25,40,27,41,26,32)(18,29,30,44,31,45,36,46)(23,37,28,43,38,39,42,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4224);