Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17390 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#121 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×Q8×C19 ◁ G | |
940 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,23,26,24,27,30,33)(22,25,29,32,28,31,34,35)(36,37,41,46,42,45,40,44)(38,47,48,51,39,43,49,50);(20,22)(21,25)(23,29)(24,28)(26,32)(27,31)(30,34)(33,35)(36,38)(37,43)(39,42)(40,48)(41,49)(44,50)(45,47)(46,51);(22,28)(25,31)(29,34)(32,35)(36,39,42,38)(37,43,45,47)(40,48,41,49)(44,51,46,50);(36,40,42,41)(37,44,45,46)(38,48,39,49)(43,50,47,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10378);