Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13234 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1964 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C13×#3058 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G | |
464 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)(14,15,20,24,21,25,19,37)(16,18,23,35,29,36,28,26)(17,30,33,39,34,44,32,22)(27,41,38,45,43,40,42,31);(14,16,26,15)(17,27,40,22)(18,24,19,28)(20,23,36,37)(21,29,35,25)(30,32,42,31)(33,38,45,44)(34,43,41,39);(14,17,20,33,21,34,19,32)(15,22,37,44,25,39,24,30)(16,27,23,38,29,43,28,42)(18,31,26,40,36,45,35,41)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6222);