Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#20444 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C2×D4 |
| commutator | C4 | C22×C42×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ C23×C8×C19 ◁ G | |
1018 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(26,34,37,47)(27,31)(28,33)(29,32)(30,36,43,40)(35,48,50,55)(38,45)(39,44)(41,46)(42,49,53,51)(52,54);(20,21,22,23)(24,26)(25,30)(27,35)(28,40)(29,37)(31,42)(32,43)(33,47)(34,46)(36,41)(38,51)(39,50)(44,53)(45,55)(48,54)(49,52);(24,27,28,38,29,39,41,52)(25,31,33,45,32,44,46,54)(26,35,40,51,37,50,36,49)(30,42,47,55,43,53,34,48);(25,32)(30,43)(31,44)(33,46)(34,47)(42,53)(45,54)(48,55)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13432);