Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32871 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
492 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)(14,15,20,22,19,25,18,24)(16,26,27,34,30,36,29,21)(17,23,31,37,33,40,32,39)(28,41,42,38,43,45,44,35);(14,16,18,29,19,30,20,27)(15,21,22,26,25,34,24,36)(17,28,31,42,33,43,32,44)(23,38,39,41,40,35,37,45);(15,22)(16,27)(17,31)(18,20)(21,34)(24,25)(28,43)(29,30)(32,33)(35,41)(37,39)(38,45);(14,17)(15,23)(16,28)(18,32)(19,33)(20,31)(21,35)(22,37)(24,39)(25,40)(26,41)(27,42)(29,44)(30,43)(34,38)(36,45)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25859);