Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10748 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C23 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #385 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1190 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)(20,21)(22,23)(24,25,28,34,30,33,29,35)(26,36,39,49,38,31,43,45)(27,32,41,46,40,48,42,47)(37,44,52,54,51,50,53,55);(24,26,29,39,30,38,28,43)(25,31,35,45,33,36,34,49)(27,37,42,52,40,51,41,53)(32,44,47,54,48,50,46,55);(21,23)(24,27)(25,32)(26,37)(28,41)(29,42)(30,40)(31,44)(33,48)(34,46)(35,47)(36,50)(38,51)(39,52)(43,53)(45,54)(49,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3736);