Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#34261 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
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)(18,19,22,23)(20,21,24,25)(26,27)(28,33)(29,32)(30,31);(19,23)(20,24)(27,31)(32,33);(14,16,17,15)(26,28,30,29)(27,32,31,33);(18,20)(19,21)(22,24)(23,25)(26,27)(28,32)(29,33)(30,31);(18,21)(19,20)(22,25)(23,24)(26,29,30,28)(27,33,31,32)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27249);