Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10747 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #379 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,28,33,29,32,41,46)(26,34,37,47,36,30,40,43)(27,31,39,44,38,45,51,55)(35,42,50,53,49,48,52,54);(20,21,22,23)(24,26)(25,30)(27,35)(28,40)(29,36)(31,42)(32,34)(33,47)(37,41)(38,49)(39,52)(43,46)(44,54)(45,48)(50,51)(53,55);(24,27)(25,31)(26,35)(28,39)(29,38)(30,42)(32,45)(33,44)(34,48)(36,49)(37,50)(40,52)(41,51)(43,53)(46,55)(47,54)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3735);