Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#9834 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #127 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(19,24)(20,25)(21,22)(26,27)(28,34)(29,37)(30,32)(31,36)(33,38)(35,40)(39,41);(15,17)(18,19,22,20,23,25,21,24)(26,28,29,36,30,35,38,41)(27,31,33,34,32,39,37,40);(18,20,22,25,23,24,21,19)(27,32)(28,35)(33,37)(36,41)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2822);