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×#34187 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C24×C13 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(20,24)(22,25)(26,27,31,29)(28,34,36,32)(30,37,38,33)(35,39,41,40);(18,19,21,23)(20,22,24,25)(27,29)(32,34)(33,37)(39,40);(18,20,21,24)(19,22,23,25)(26,28,31,36)(27,32,29,34)(30,35,38,41)(33,39,37,40);(26,29,31,27)(28,34,36,32)(30,37,38,33)(35,40,41,39);(26,30)(27,33)(28,35)(29,37)(31,38)(32,39)(34,40)(36,41)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27175);