Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2180 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C2×C13×AGL(1,ℤ/16) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #442 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#97 ◁ G | |
710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(4,8,10,17)(5,12)(6,13)(9,15,18,11)(14,16);(3,4)(5,9)(6,15)(7,10)(8,16)(11,13)(12,17)(14,18);(3,5,13,16,7,14,6,12)(4,9,11,8,10,18,15,17)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26455);