Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33688 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C4×C13×M16 ◁ G | |
564 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)(15,19)(16,23)(17,26)(20,25)(21,27)(22,28)(24,29);(16,24)(19,27)(23,29)(25,28);(14,15)(16,25)(17,20)(18,21)(19,23)(22,26)(24,28)(27,29);(15,20,21,22)(16,24)(19,25,27,28)(23,29)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26676);