Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#12036 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D8 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| socle | C22×C19 | C2×#107 |
| prime radical | C23×C19 | #107 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,26,24,27,30,33)(22,25,29,32,28,31,34,35)(36,37)(38,46)(39,43)(40,49)(41,51)(42,45)(44,47)(48,50);(20,22)(21,25)(23,29)(24,28)(26,32)(27,31)(30,34)(33,35)(36,38,47,45,41,48,50,51,42,44,46,37,39,49,40,43);(22,28)(25,31)(29,34)(32,35)(36,39,42,41)(37,43,45,51)(38,48,44,49)(40,46,50,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5024);