Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21782 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#21782 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2308 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3498 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,23,25,19)(17,22)(18,21)(20,24,29,26)(27,28);(14,16)(15,19)(17,26)(18,25)(20,28)(21,23)(22,29)(24,27);(14,16)(15,20)(17,26)(18,25)(19,22)(21,29)(23,28)(24,27);(14,16)(15,19)(17,24)(18,25)(20,22)(21,23)(26,27)(28,29)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 14770);