Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34236 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2750 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,22,20)(21,24,25,23)(26,27,30,29)(28,32,33,31);(14,16,17,15)(19,20)(23,24)(27,29)(31,32);(26,28)(27,31)(29,32)(30,33);(18,20,22,19)(21,24,25,23)(26,29,30,27)(28,32,33,31);(18,21,22,25)(19,23,20,24)(26,28)(27,31)(29,32)(30,33)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27224);