Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25143 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,23,28,24,29,22,27)(20,25,32,41,33,42,31,40)(21,34,36,44,37,45,38,26)(30,46,47,43,35,49,48,39);(15,17)(18,20,23,32,24,33,22,31)(19,25,28,41,29,42,27,40)(21,35,36,48,37,30,38,47)(26,43,34,49,44,39,45,46);(18,21,24,37)(19,26,29,44)(20,30,33,35)(22,36,23,38)(25,39,42,43)(27,34,28,45)(31,47,32,48)(40,46,41,49);(15,17)(18,22,24,23)(19,27,29,28)(20,31,33,32)(21,36,37,38)(25,40,42,41)(26,34,44,45)(30,47,35,48)(39,46,43,49)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18131);