Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1946 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,30,35)(26,36,38,48)(27,40,42,49)(28,34,29,33)(31,43,46,39)(32,44,47,41)(37,45,51,55)(50,52,54,53);(20,21)(22,23)(24,26)(25,31)(27,37)(28,43)(29,39)(30,38)(32,45)(33,48)(34,36)(35,46)(40,54)(41,53)(42,51)(44,52)(47,55)(49,50);(21,23)(24,27)(25,32)(26,37)(28,41)(29,44)(30,42)(31,45)(33,40)(34,49)(35,47)(36,50)(38,51)(39,52)(43,53)(46,55)(48,54);(26,38)(31,46)(36,48)(37,51)(39,43)(45,55)(50,54)(52,53)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16396);