Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33797 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
460 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,26)(23,25)(24,27)(28,29,34,38)(30,39,42,57)(31,36,33,48)(32,44,47,58)(35,50,53,41)(37,43,55,46)(40,56,49,54)(45,51,59,52);(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25);(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26)(28,30)(29,35)(31,40)(32,45)(33,49)(34,42)(36,51)(37,54)(38,53)(39,44)(41,46)(43,50)(47,59)(48,52)(55,56)(57,58);(13,19)(17,20)(18,27)(25,26)(28,31,34,33)(29,36,38,48)(30,40,42,49)(32,43,47,46)(35,51,53,52)(37,44,55,58)(39,56,57,54)(41,45,50,59)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26785);