Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#22257 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C23×C11 | C2×#41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,19)(16,25)(17,20)(18,23)(22,27)(24,26)(28,29,33,37,34,38,32,47)(30,35,41,49,42,50,40,56)(31,43,46,51,44,57,45,36)(39,52,55,58,53,59,54,48);(12,14)(13,18)(15,24)(16,22)(17,23)(19,27)(20,21)(25,26)(28,30,33,41,34,42,32,40)(29,35,37,49,38,50,47,56)(31,39,46,55,44,53,45,54)(36,48,43,52,51,58,57,59);(12,15,17,16)(13,19,20,25)(14,22,23,24)(18,26,21,27)(28,31,32,45,34,44,33,46)(29,36,37,43,38,51,47,57)(30,39,40,54,42,53,41,55)(35,48,49,52,50,58,56,59);(12,16,17,15)(13,19,20,25)(14,22,23,24)(18,27,21,26)(31,44)(36,51)(39,53)(43,57)(45,46)(48,58)(52,59)(54,55)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15245);