Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#17607 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3494 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
990 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)(22,28,30,25)(23,26)(24,27)(29,34,35,32)(31,33)(36,37)(38,43)(39,44)(40,49)(41,45)(42,46)(47,50)(48,51);(20,22)(21,25)(23,29)(24,30)(26,32)(27,28)(31,35)(33,34)(36,38)(37,42)(39,46)(40,48)(41,47)(43,49)(44,50)(45,51);(20,23,24,31)(21,26,27,33)(22,29,30,35)(25,32,28,34)(36,38)(37,43)(39,48)(40,46)(41,47)(42,49)(44,51)(45,50);(36,39,41,40)(37,44,45,49)(38,46,47,48)(42,50,51,43)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10595);