Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#36699 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
1958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,24)(21,25)(22,23)(26,29)(27,31)(28,30)(32,33)(34,35,38,41)(36,39,43,47)(37,40,45,49)(42,46,44,48);(19,23)(24,29)(25,30)(31,33)(34,36,38,43)(35,39,41,47)(37,44,45,42)(40,48,49,46);(15,17)(18,20)(19,24)(21,27)(22,26)(23,29)(25,31)(28,32)(30,33)(34,37)(35,40)(36,42)(38,45)(39,46)(41,49)(43,44)(47,48);(20,26)(24,29)(27,32)(31,33)(35,41)(37,45)(39,47)(42,44);(18,21,22,28)(19,25,23,30)(20,27,26,32)(24,31,29,33)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29687);