Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C24×C13 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G | |
512 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)(18,19,22,28,36,44,37,46,24,26,21,27,23,29,39,48)(20,30,33,43,40,47,35,25,32,42,31,49,34,45,38,41);(14,15,16,17)(18,20)(19,25)(21,35)(22,38)(23,40)(24,32)(26,41)(27,45)(28,47)(29,49)(30,46)(31,37)(33,39)(34,36)(42,48)(43,44);(19,26)(21,22)(25,41)(29,44)(31,33)(35,38)(37,39)(43,49)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5988);