Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12077 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13039 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #442 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G | |
472 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,24,30,34,49,22,41,26,32,23,43,25,31,42,29)(20,33,35,47,44,28,40,46,37,48,39,27,36,45,21,38);(14,15,16,17)(18,20,34,36,26,37,25,44)(19,27,31,38,32,47,49,46)(21,22,39,23,40,42,35,24)(28,30,48,29,45,43,33,41);(18,21)(19,28)(20,22)(23,36)(24,44)(25,35)(26,40)(27,30)(29,38)(31,48)(32,45)(33,49)(34,39)(37,42)(41,46)(43,47)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6027);