Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1364 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,30,32,26)(23,27)(24,29)(25,28)(31,40,49,48)(33,46,37,41)(34,42,50,51)(35,44)(36,43)(38,47)(39,45);(20,22)(21,26)(23,34)(24,37)(25,32)(27,42)(28,30)(29,46)(31,36)(33,39)(35,50)(38,49)(40,43)(41,45)(44,51)(47,48);(20,23)(21,27)(22,31)(24,38)(25,35)(26,40)(28,44)(29,47)(30,48)(32,49)(33,50)(34,37)(36,39)(41,51)(42,46)(43,45);(20,22)(21,26)(23,31)(24,33)(25,32)(27,40)(28,30)(29,41)(34,36)(35,49)(37,39)(38,50)(42,43)(44,48)(45,46)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17396);