Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#8134 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C19 | C23 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| socle, prime radical | C23×C19 | C2×C42 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C19 ◁ G | |
414 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)(28,29,31,35,33,34,32,30)(36,37,39,42,40,43,46,49)(38,41,45,48,44,47,50,51);(21,24)(25,27)(28,30,32,34,33,35,31,29)(36,38)(37,41)(39,45)(40,44)(42,48)(43,47)(46,50)(49,51);(20,22,23,26)(21,25,24,27)(29,34)(30,35)(38,44)(41,47)(45,50)(48,51)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1122);