Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C2×C13×#2444 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C22×C13×#121 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
3546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35);(7,8)(9,11)(10,13)(12,14)(15,16)(17,21)(18,20)(19,22);(4,6)(8,9)(12,13)(15,16,18,20)(17,19,22,21);(3,4)(5,6)(7,9,11,8)(10,13,14,12)(15,16)(17,19)(18,20)(21,22);(7,10)(8,12)(9,13)(11,14)(15,17)(16,19)(18,22)(20,21)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27656);