Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24340 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×Q8×C13 ◁ G | |
1036 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,25)(20,24,21,23)(26,27,30,34)(28,36,39,32)(29,35,31,33)(37,41,38,40);(18,20,22,21)(19,23,25,24)(26,28)(27,32)(29,38)(30,39)(31,37)(33,40)(34,36)(35,41);(15,17)(27,33)(28,37)(29,31)(34,35)(38,39)(40,41);(18,21,22,20)(19,24,25,23)(26,29,30,31)(27,33,34,35)(28,38,39,37)(32,40,36,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17328);