Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#11950 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C4×C8 | C23×C19 |
| socle | C22×C19 | C2×#102 |
| prime radical | C23×C19 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
300 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,28,23,27)(22,30,31,35,32,26,33,34)(36,37,40,45,42,47,55,44,41,46,56,63,54,62,39,53)(38,48,50,59,52,61,66,65,51,64,67,43,57,58,49,60);(20,22)(21,26)(23,31)(24,33)(25,32)(27,34)(28,30)(29,35)(36,38,41,51)(37,43,46,59)(39,50,55,67)(40,49,56,66)(42,57,54,52)(44,61,53,58)(45,64,63,48)(47,65,62,60);(20,23,25,24)(21,27,28,29)(22,31,32,33)(26,34,30,35)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4938);