Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#22687 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×C4⋊C8 ◁ G | |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,23,25,24,20,21,27)(22,26,32,33,31,28,29,30);(18,20)(19,24)(21,25)(22,30)(23,27)(26,32)(28,29)(31,33);(14,15,16,17)(18,21,24,23)(19,25,20,27)(22,29,31,32)(26,33,28,30);(18,22)(19,26)(20,28)(21,29)(23,32)(24,31)(25,33)(27,30)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15675);