Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8489 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3560 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21,23,18)(15,17)(16,20)(19,24)(22,26,27,25)(28,29,32,37,33,36,47,51)(30,38,41,52,40,34,45,49)(31,42,44,53,43,35,46,50)(39,54,56,59,55,48,57,58);(13,17)(15,24)(18,25)(19,20)(21,26)(22,27)(28,30)(29,34)(31,39)(32,45)(33,40)(35,48)(36,38)(37,52)(41,47)(42,54)(43,55)(44,57)(46,56)(49,51)(50,59)(53,58);(12,14)(13,18)(15,22)(16,23)(17,25)(19,26)(20,21)(24,27)(28,31)(29,35)(30,39)(32,46)(33,43)(34,48)(36,42)(37,53)(38,54)(40,55)(41,57)(44,47)(45,56)(49,59)(50,51)(52,58)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1477);