Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#13113 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D8 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C4×D8 |
| prime radical | C23×C19 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×C8×C19 ◁ C2×C4×C8×C19 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(28,29,34,39,32,37,48,40)(30,38,43,52,42,35,33,49)(31,44,46,56,45,59,47,51)(36,53,55,58,54,50,57,41);(21,24)(25,27)(28,30,34,43,32,42,48,33)(29,35,39,49,37,38,40,52)(31,41,46,53,45,58,47,50)(36,51,55,44,54,56,57,59);(20,22,23,26)(21,25,24,27)(28,31,32,45)(29,36,37,54)(30,41,42,58)(33,50,43,53)(34,46,48,47)(35,51,38,56)(39,55,40,57)(44,52,59,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6101);