Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17521 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C22×C22⋊C4 |
| prime radical | C19×#3481 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×#41×C19 ◁ G | |
1010 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)(22,29)(23,25)(24,28)(26,30)(27,32)(31,34)(33,35)(36,37,40,44,41,43,39,48)(38,45,46,42,47,51,49,50);(21,25)(23,32)(26,33)(27,28)(29,34)(31,35)(36,38)(37,42)(39,49)(40,46)(41,47)(43,50)(44,51)(45,48);(20,22)(21,26)(23,31)(24,30)(25,33)(27,34)(28,29)(32,35)(37,43)(42,50)(44,48)(45,51);(22,30)(26,29)(31,35)(33,34)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10509);