Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11858 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
394 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)(22,26,27,24)(23,25)(28,29,33,39,35,41,34,40)(30,42,45,57,47,58,46,53)(31,48,32,51,50,38,49,37)(36,52,54,44,56,43,55,59);(20,22)(21,24)(23,27)(25,26)(28,30)(29,36)(31,44)(32,52)(33,46)(34,45)(35,47)(37,42)(38,57)(39,55)(40,54)(41,56)(43,49)(48,53)(50,59)(51,58);(22,27)(24,26)(28,31,34,49,35,50,33,32)(29,37,39,48,41,51,40,38)(30,43,46,44,47,52,45,59)(36,53,54,42,56,57,55,58)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4882);