Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G | |
1030 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
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)(20,21,22,23)(24,25)(26,32)(27,30)(28,31)(29,34)(33,38)(35,37)(36,39)(40,41)(42,50)(43,49)(44,46)(45,48)(47,52)(51,55)(53,54);(24,26,28,34)(25,29,31,32)(27,35,36,33)(30,38,39,37)(41,46)(42,51)(48,49)(52,53);(24,27,28,36)(25,30,31,39)(26,33,34,35)(29,37,32,38)(40,42,44,51)(41,47,46,54)(43,52,45,53)(48,50,49,55);(25,31)(29,32)(30,39)(37,38)(40,43,44,45)(41,48,46,49)(42,52,51,53)(47,50,54,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14825);