Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13394 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,25,31)(20,32,35,44)(21,36,33,26)(22,30,24,28)(23,39,42,48)(27,45,47,37)(29,38,49,41)(34,46,40,43);(14,15)(16,17)(18,20)(19,26)(21,22)(23,40)(24,33)(25,35)(27,39)(28,44)(29,46)(30,32)(31,36)(34,42)(37,41)(38,45)(43,49)(47,48);(15,17)(18,21,22,20,25,33,24,35)(19,27,28,43,31,47,30,46)(23,40,38,37,42,34,41,45)(26,29,32,48,36,49,44,39)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6382);