Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#12988 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1869 |
| prime radical | C19×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
466 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)(20,21,25,31,26,29,43,46,27,30,44,48,24,41,33,50)(22,32,36,42,37,47,51,23,35,39,49,38,34,28,45,40);(20,22,33,45,24,34,44,49,27,35,43,51,26,37,25,36)(21,28,46,42,41,39,31,40,30,47,50,38,29,32,48,23);(20,23)(21,22)(24,42)(25,32)(26,38)(27,40)(28,33)(29,37)(30,35)(31,49)(34,41)(36,48)(39,44)(43,47)(45,46)(50,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5976);