Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13270 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #124 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1985 |
| prime radical | C23×C13 | C2×M16 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
316 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)(14,15,19,25,20,24,36,39,21,26,37,43,18,32,28,44)(16,27,31,35,30,40,45,33,29,22,38,34,23,41,42,17);(14,16,28,42,18,23,37,38,21,29,36,45,20,30,19,31)(15,22,39,17,32,40,25,34,26,27,44,33,24,41,43,35);(14,17,18,34,21,33,20,35)(15,23,24,16,26,30,32,29)(19,27,28,41,37,22,36,40)(25,42,39,31,43,45,44,38)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6258);