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×#11943 |
| 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 | C19×#466 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
306 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)(36,37,40,45,41,46,55,63,42,47,56,64,54,62,39,44)(38,48,50,60,51,61,49,65,52,66,53,43,57,58,67,59);(20,22)(21,26)(23,31)(24,33)(25,32)(27,34)(28,30)(29,35)(36,38)(37,43)(39,53)(40,49)(41,57)(42,52)(44,61)(45,48)(46,65)(47,60)(50,55)(51,54)(56,67)(58,63)(59,62)(64,66);(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, 4931);