Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#8485 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#121 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
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)(21,25,27,30)(26,34,35,33)(36,37,40,45,41,44,55,59)(38,46,49,60,48,42,53,57)(39,50,52,61,51,43,54,58)(47,62,64,67,63,56,65,66);(20,21)(22,26)(23,30)(24,27)(25,32)(28,33)(29,35)(31,34)(36,38)(37,42)(39,47)(40,53)(41,48)(43,56)(44,46)(45,60)(49,55)(50,62)(51,63)(52,65)(54,64)(57,59)(58,67)(61,66);(20,22,24,29)(21,26,27,35)(23,31,32,28)(25,33,30,34)(36,39)(37,43)(38,47)(40,54)(41,51)(42,56)(44,50)(45,61)(46,62)(48,63)(49,65)(52,55)(53,64)(57,67)(58,59)(60,66)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1473);