Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11943 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C11×#466 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
306 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)(12,13,16,21,17,20,15,19)(14,22,23,27,24,18,25,26)(28,29,32,37,33,38,47,55,34,39,48,56,46,54,31,36)(30,40,42,52,43,53,41,57,44,58,45,35,49,50,59,51);(12,14)(13,18)(15,23)(16,25)(17,24)(19,26)(20,22)(21,27)(28,30)(29,35)(31,45)(32,41)(33,49)(34,44)(36,53)(37,40)(38,57)(39,52)(42,47)(43,46)(48,59)(50,55)(51,54)(56,58);(12,15,17,16)(13,19,20,21)(14,23,24,25)(18,26,22,27)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4931);