Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61083 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
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)(18,19,24,29)(20,30,34,45)(21,26,36,43)(22,28,23,27)(25,38,41,33)(31,46,49,40)(32,47,48,39)(35,44,37,42);(18,20,24,34)(19,25,29,41)(21,31,36,49)(22,33,23,38)(26,39,43,47)(27,30,28,45)(32,37,48,35)(40,44,46,42);(15,17)(18,21)(19,26)(20,31)(22,37)(23,35)(24,36)(25,39)(27,44)(28,42)(29,43)(30,46)(32,38)(33,48)(34,49)(40,45)(41,47);(18,21)(19,26)(20,32)(22,35)(23,37)(24,36)(25,40)(27,42)(28,44)(29,43)(30,47)(31,38)(33,49)(34,48)(39,45)(41,46);(18,22,24,23)(19,27,29,28)(20,33,34,38)(21,35,36,37)(25,30,41,45)(26,42,43,44)(31,32,49,48)(39,40,47,46)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54071);