Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17367 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#20639 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
1314 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)(21,23)(24,25,28,33,29,32,41,46)(26,30,36,44,35,43,51,54)(27,37,38,47,39,31,40,45)(34,48,50,55,49,42,52,53);(20,21,22,23)(24,26)(25,30)(27,34)(28,36)(29,35)(31,42)(32,43)(33,44)(37,48)(38,50)(39,49)(40,52)(41,51)(45,53)(46,54)(47,55);(24,27,29,39)(25,31,32,37)(26,34,35,49)(28,40,41,38)(30,42,43,48)(33,47,46,45)(36,52,51,50)(44,55,54,53);(26,35)(30,43)(34,49)(36,51)(42,48)(44,54)(50,52)(53,55)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13627);