Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13005 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1874 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,24,20,26,35,38,21,27,17,33,18,25,34,22)(16,28,31,37,30,41,45,42,32,43,29,44,36,23,39,40);(15,22,27,38)(17,34)(18,20)(19,35)(23,37,41,44)(24,26,33,25)(28,40,43,42)(29,39)(30,36)(31,45);(14,16)(15,23)(17,31)(18,36)(19,29)(20,30)(21,32)(22,37)(24,42)(25,43)(26,28)(27,41)(33,40)(34,45)(35,39)(38,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5993);