Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#13106 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C19 | C2×D4 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C22×C19 | C8×D4 |
| prime radical | C23×C19 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C19 ◁ C22×C16×C19 ◁ G | |
272 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)(28,29,34,39,33,40,50,57,32,37,49,41,48,38,55,56)(30,31,44,46,43,47,54,59,42,35,51,52,58,45,36,53);(21,24)(25,27)(28,30,34,44,33,43,50,54,32,42,49,51,48,58,55,36)(29,35,39,52,40,45,57,53,37,31,41,46,38,47,56,59);(20,22,23,26)(21,25,24,27)(28,31,32,35)(29,36,37,54)(30,41,42,39)(33,47,48,45)(34,46,49,52)(38,51,40,44)(43,56,58,57)(50,59,55,53)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6094);