Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19087 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3558 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
930 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)(20,21,24,26)(22,28,29,35)(23,31,33,27)(25,32,34,30)(36,37)(38,44)(39,47)(40,42)(41,46)(43,48)(45,51)(49,50);(20,22)(21,25)(23,32)(24,29)(26,34)(27,35)(28,31)(30,33)(39,48)(43,47)(44,51)(46,49);(23,33)(27,31)(28,35)(30,32)(36,38)(37,41)(39,49)(40,45)(42,50)(43,51)(44,47)(46,48);(21,26)(22,29)(27,31)(30,32)(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, 12075);