Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #20671 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33426 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C2×#117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C2×#432 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×C19×#97 ◁ G | |
520 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)(20,21,23,29,24,30,37,46,25,28,36,44,38,27,42,43)(22,31,33,45,34,39,48,50,32,26,35,40,47,41,49,51);(20,22)(21,26)(23,35)(24,34)(25,32)(27,39)(28,31)(29,45)(30,41)(33,36)(37,49)(38,47)(40,44)(42,48)(43,51)(46,50);(21,27,28,30)(23,36)(26,39,31,41)(29,46,44,43)(33,35)(37,42)(40,51,45,50)(48,49);(22,32)(26,31)(33,35)(34,47)(39,41)(40,45)(48,49)(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, 26414);