Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12767 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#12770 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1790 |
| commutator | C2×D4 | C22×C4×C19 |
| Frattini, cosocle | C2×#41 | C23×C19 |
| prime radical | C19×#3551 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
752 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,27,37,42)(22,30,33,46,32,47,50,51)(23,34,36,45,35,28,38,43)(26,39,41,31,40,48,44,49);(20,22,25,32)(21,26,27,40)(23,31,35,49)(24,33,37,50)(28,30,34,47)(29,44,42,41)(36,48,38,39)(43,51,45,46);(21,27)(24,37)(26,40)(33,50)(36,38)(39,48)(43,45)(46,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5758);