Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C2×C13×#2018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G | |
2158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4)(5,6)(7,8)(9,17)(10,15)(11,14)(12,16)(13,18)(19,22)(20,21);(4,6)(7,9)(8,13)(10,19)(11,18)(12,20)(14,21)(15,17)(16,22);(8,14)(9,18)(10,11)(15,16)(17,21)(19,20)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16423);