Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#8279 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle, prime radical | C23×C13 | C2×C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C43×C13 ◁ G | |
394 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)(14,15,17,16)(18,19,21,23,22,24,20,25)(26,27)(28,31)(29,33)(30,32)(34,38)(35,37)(36,39)(40,41);(19,23)(20,21)(24,25)(26,28,29,34,30,35,36,40)(27,31,33,38,32,37,39,41);(14,16,17,15)(19,24)(23,25)(27,32)(31,37)(33,39)(38,41)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1267);