Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61110 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
2684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,23)(16,25,21,28)(17,27,18,22)(19,26,29,24);(14,16)(15,18)(17,23)(19,22)(20,21)(24,28)(25,26)(27,29);(14,17)(15,21)(16,23)(18,20)(19,28)(22,24)(25,29)(26,27);(14,18)(15,22)(16,26)(17,20)(19,28)(21,24)(23,27)(25,29);(15,23)(16,21)(22,27)(24,26)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54098);