Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#11973 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| prime radical | C23×C19 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
288 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)(20,21,23,27,24,26,32,34)(22,28,29,35,30,25,31,33)(36,37,41,46,39,48,55,45,42,47,58,63,56,44,40,57)(38,49,52,61,54,62,67,65,53,64,66,43,50,60,51,59);(20,22,24,30)(21,25,26,28)(23,31,32,29)(27,35,34,33)(36,38,42,53)(37,43,47,61)(39,50,56,54)(40,52,55,66)(41,51,58,67)(44,59,48,65)(45,62,57,60)(46,64,63,49);(21,26)(25,28)(27,34)(33,35)(36,39,42,56)(37,44,47,48)(38,50,53,54)(40,41,55,58)(43,59,61,65)(45,46,57,63)(49,62,64,60)(51,66,67,52)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4961);