Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11973 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| prime radical | C23×C11 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
288 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,19,16,18,24,26)(14,20,21,27,22,17,23,25)(28,29,33,38,31,40,47,37,34,39,50,55,48,36,32,49)(30,41,44,53,46,54,59,57,45,56,58,35,42,52,43,51);(12,14,16,22)(13,17,18,20)(15,23,24,21)(19,27,26,25)(28,30,34,45)(29,35,39,53)(31,42,48,46)(32,44,47,58)(33,43,50,59)(36,51,40,57)(37,54,49,52)(38,56,55,41);(13,18)(17,20)(19,26)(25,27)(28,31,34,48)(29,36,39,40)(30,42,45,46)(32,33,47,50)(35,51,53,57)(37,38,49,55)(41,54,56,52)(43,58,59,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4961);