Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11712 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C24×C19 | SD16 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
440 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26,27,24)(23,25)(28,29,31,36,34,39,33,38)(30,40,41,54,44,57,43,56)(32,46,45,37,49,53,48,55)(35,47,50,42,52,58,51,59);(20,22)(21,24)(23,27)(25,26)(28,30,34,44)(29,35,39,52)(31,43,33,41)(32,47,49,58)(36,51,38,50)(37,54,55,56)(40,46,57,53)(42,45,59,48);(28,31,34,33)(29,36,39,38)(30,41,44,43)(32,45,49,48)(35,50,52,51)(37,53,55,46)(40,54,57,56)(42,58,59,47)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4700);