Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10782 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #120 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #386 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1178 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)(24,25,28,34,30,35,29,33)(26,36,39,47,40,46,38,31)(27,41,43,48,44,49,42,32)(37,45,51,54,52,55,53,50);(24,26,29,38,30,40,28,39)(25,31,33,46,35,47,34,36)(27,37,43,51,44,52,42,53)(32,45,41,54,48,55,49,50);(21,23)(24,27)(25,32)(26,37)(28,42)(29,43)(30,44)(31,45)(33,41)(34,49)(35,48)(36,50)(38,51)(39,53)(40,52)(46,54)(47,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3770);