Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1324 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,26,21,27,20,25)(16,28,32,41,33,43,31,22)(17,34,37,24,18,38,36,23)(29,39,35,42,44,45,30,40);(14,16)(15,22)(17,35)(18,30)(19,32)(20,31)(21,33)(23,42)(24,40)(25,43)(26,28)(27,41)(29,36)(34,45)(37,44)(38,39);(14,17,21,18)(15,23,27,24)(16,29,33,44)(19,36,20,37)(22,39,41,45)(25,34,26,38)(28,40,43,42)(30,31,35,32);(14,18,21,17)(15,24,27,23)(16,30,33,35)(19,36,20,37)(22,40,41,42)(25,34,26,38)(28,39,43,45)(29,31,44,32)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17463);