Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#9088 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
480 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(20,21,23,26,24,22,25,27)(28,29)(30,39)(31,43,46,53)(32,47)(33,37)(34,38)(35,41)(36,45,52,44)(40,55,57,49)(42,50)(48,51)(54,56,59,58);(20,22,23,27,24,21,25,26)(28,30,32,41,34,42,33,48)(29,35,37,39,38,51,47,50)(31,40,45,58,46,57,44,56)(36,49,53,54,52,55,43,59);(28,31,34,46)(29,36,38,52)(30,40,42,57)(32,45,33,44)(35,49,51,55)(37,53,47,43)(39,54,50,59)(41,58,48,56)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2076);