Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7606 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7644 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C43×C19 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
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)(20,21,22,25,23,24,26,27)(28,29,32,35,33,30,31,34)(36,37)(38,44,46,41)(39,47)(40,43)(42,48)(45,49,51,50);(28,30,33,29)(31,34,32,35)(36,38)(37,41)(39,45)(40,46)(42,49)(43,44)(47,50)(48,51);(21,24)(25,27)(36,39,40,48)(37,42,43,47)(38,45,46,51)(41,49,44,50)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 632);