Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32699 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2749 |
| 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 | |
538 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)(14,15,20,25,19,24,32,40)(16,17,22,29,27,21,33,36)(18,23,31,39,30,38,34,41)(26,35,42,45,43,28,37,44);(14,16)(15,21)(17,24)(18,26)(19,27)(20,33)(22,32)(23,28)(25,29)(30,43)(31,37)(34,42)(35,38)(36,40)(39,45)(41,44);(14,17)(15,22,24,33)(16,25,27,40)(18,28)(19,21)(20,29)(23,37,38,42)(26,41,43,39)(30,35)(31,44)(32,36)(34,45);(14,18,19,30)(15,23,24,38)(16,26,27,43)(17,28,21,35)(20,34,32,31)(22,37,33,42)(25,41,40,39)(29,45,36,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25687);