Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12026 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#12911 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #427 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1846 |
| prime radical | C23×C19 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
266 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,33,37,57)(23,39,42,69)(24,44)(25,31)(26,48)(27,32)(28,35,51,64)(29,41,53,43)(30,46)(34,58)(36,56,38,66)(40,70,72,52)(45,54)(47,74)(49,76)(50,63,75,65)(55,61)(59,80)(60,78)(62,79)(67,82)(68,71,83,73)(77,81);(20,22,24,35,26,38,46,65,27,37,47,64,25,36,45,63)(21,28,30,33,31,50,44,56,32,51,54,57,48,75,74,66)(23,34,40,59,43,61,73,81,42,62,72,82,41,60,71,76)(29,49,52,55,39,67,68,58,53,77,70,78,69,80,83,79);(20,23)(21,29,32,53)(22,34)(24,40)(25,41)(26,43)(27,42)(28,49,51,77)(30,52,54,70)(31,39,48,69)(33,55,57,78)(35,59)(36,60)(37,62)(38,61)(44,68,74,83)(45,71)(46,73)(47,72)(50,67,75,80)(56,58,66,79)(63,76)(64,82)(65,81)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5899);