Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12792 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #121 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1797 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C22×C8×C19 ◁ G | |
440 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)(20,21,25,32,26,30,37,45,27,33,36,28,24,31,22,34)(23,38,41,50,40,47,35,49,42,48,43,51,39,29,46,44);(20,22,24,36,27,37,26,25)(21,28,30,34,33,32,31,45)(23,35,39,41,42,46,40,43)(29,44,38,50,47,49,48,51);(20,23)(21,29)(22,35)(24,39)(25,43)(26,40)(27,42)(28,44)(30,38)(31,48)(32,49)(33,47)(34,50)(36,41)(37,46)(45,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5780);