Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11858 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#11987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| prime radical | C23×C19 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
300 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(22,23)(26,27)(28,29,32,38,46,54,47,56,34,36,31,37,33,39,49,58)(30,40,42,53,50,57,45,35,44,52,41,59,43,55,48,51);(20,21)(22,25)(23,27)(24,26)(28,30,34,44)(29,35,36,51)(31,45,32,48)(33,50,46,43)(37,55,38,57)(39,59,54,53)(40,58,52,56)(41,49,42,47);(20,22,24,23)(21,25,26,27)(29,36)(35,51)(37,38)(39,54)(40,52)(53,59)(55,57)(56,58)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4975);