Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13144 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
334 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)(14,15,17,16)(19,24)(20,29)(21,25)(22,33)(26,41)(27,44)(28,38)(30,32)(31,39)(34,40)(35,42)(36,37)(43,47)(45,46);(14,16,17,15)(18,19,25,37,22,27,34,38,23,28,40,44,33,36,21,24)(20,26,39,48,31,41,29,42,32,43,46,49,45,47,30,35);(18,20,21,30,33,45,40,46,23,32,34,29,22,31,25,39)(19,26,24,35,36,47,44,49,28,43,38,42,27,41,37,48)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6132);