Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33372 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#99 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×Q8 | C24×C19 |
| prime radical | C19×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×D4×C19 ◁ C2×C19×2−1+4 ◁ G | |
1176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(20,21,25,30,26,31,22,32)(23,28,37,44,35,42,33,46)(24,29,34,41,39,45,38,27)(36,43,47,50,48,51,49,40);(20,22,26,25)(21,27,31,41)(23,33,35,37)(24,38,39,34)(28,40,42,50)(29,30,45,32)(36,49,48,47)(43,44,51,46);(20,23)(21,28)(22,33)(24,36)(25,37)(26,35)(27,40)(29,43)(30,44)(31,42)(32,46)(34,47)(38,49)(39,48)(41,50)(45,51);(23,35)(28,42)(33,37)(36,48)(40,50)(43,51)(44,46)(47,49)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26360);