Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#7673 |
| 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 | |
384 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)(21,24)(22,26)(25,27)(29,33,34,35)(36,37,39,43,40,42,48,50)(38,44,46,51,45,41,47,49);(20,21,23,25)(22,27,26,24)(28,29)(30,33)(31,35)(32,34)(36,38,40,45)(37,41,42,44)(39,47,48,46)(43,51,50,49);(28,30,32,31)(29,33,34,35)(38,45)(41,44)(46,47)(49,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 661);