Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19090 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,26)(23,24)(27,34)(28,29)(30,32)(33,35)(36,37)(38,44)(39,47)(40,42)(41,46)(43,48)(45,51)(49,50);(20,21,25,29)(22,27,31,35)(23,26,24,28)(30,33,32,34)(39,48)(43,47)(44,51)(46,49);(20,22)(21,27)(23,30)(24,32)(25,31)(26,33)(28,34)(29,35)(36,38)(37,41)(39,49)(40,45)(42,50)(43,51)(44,47)(46,48);(20,23,25,24)(21,28,29,26)(22,30,31,32)(27,34,35,33)(37,42)(41,50)(43,47)(44,51)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12078);