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×#33799 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
466 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)(30,40)(31,39)(32,35)(33,46)(34,37)(36,43)(38,48)(41,56)(42,58)(44,51)(45,53)(47,55)(49,54)(50,57)(52,59);(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25)(29,35)(30,41)(37,39)(38,51)(42,49)(43,57)(46,53)(47,59);(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26)(28,30,32,41)(29,36,35,50)(31,42,34,49)(33,47,45,59)(37,52,39,55)(38,54,51,58)(40,53,56,46)(43,44,57,48);(13,19)(17,20)(18,27)(25,26)(28,31,32,34)(29,37,35,39)(30,42,41,49)(33,44,45,48)(36,52,50,55)(38,53,51,46)(40,54,56,58)(43,47,57,59)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26787);