Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C2×C8 |
| direct product | C19×#8158 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle | C22×C19 | C4×C22⋊C4 |
| prime radical | C24×C19 | C42 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,27)(24,26)(28,32)(29,31)(30,33)(34,35)(36,37,40,44,41,45,52,58)(38,46,49,60,48,42,53,55)(39,43,50,56,51,57,63,66)(47,59,62,67,61,54,64,65);(20,22,23,28,24,29,30,34)(21,25,27,32,26,31,33,35)(36,38)(37,42,45,46)(39,47)(40,49)(41,48)(43,54,57,59)(44,55,58,60)(50,62)(51,61)(52,53)(56,65,66,67)(63,64);(21,26)(25,31)(27,33)(32,35)(36,39,40,50,41,51,52,63)(37,43,44,56,45,57,58,66)(38,47,49,62,48,61,53,64)(42,54,55,65,46,59,60,67)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1146);