Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#17991 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C23×C19 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C19×#431 ◁ G | |
544 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,28,25,27,33,34)(22,26,30,23,29,31,35,32)(36,37)(38,46)(39,43)(40,52)(41,44)(42,48)(45,54)(47,60)(49,59)(50,58)(51,64)(53,56)(55,62)(57,63)(61,67)(65,66);(20,22)(21,26)(23,28)(24,30)(25,29)(27,31)(32,34)(33,35)(36,38,41,49)(37,42,44,56)(39,47,50,61)(40,53,54,48)(43,55,58,66)(45,59,52,46)(51,65,63,62)(57,67,64,60);(20,23,24,31,25,32,33,26)(21,22,28,30,27,29,34,35)(36,39,41,50)(37,43,44,58)(38,47,49,61)(40,51,54,63)(42,55,56,66)(45,57,52,64)(46,60,59,67)(48,62,53,65);(21,27)(22,29)(28,34)(30,35)(37,44)(39,50)(42,56)(45,52)(46,59)(47,61)(51,63)(62,65)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10979);