Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#8901 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #385 |
| prime radical | C2×C13×#41 | Q8 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21,19,22,17,26)(16,23,24,20,25,28,27,29)(30,31,34,37)(32,38,39,45)(33,41,42,36)(35,43,44,40);(14,16,18,24,19,25,17,27)(15,20,21,28,22,29,26,23)(33,42)(36,41)(38,45)(40,43);(30,32,34,39)(31,35,37,44)(33,43,42,40)(36,45,41,38)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1889);