Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26789 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G | |
804 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19)(20,25)(21,23)(22,24)(26,27)(28,31)(29,32)(30,33)(34,41)(35,39)(36,38)(37,40);(14,15,17,16)(18,20,22,21)(19,23,24,25)(26,28,29,35)(27,31,32,39)(30,34,37,36)(33,41,40,38);(14,15,17,16)(18,21,22,20)(19,23,24,25)(27,32)(28,34)(30,37)(31,38)(35,36)(39,41);(14,16,17,15)(19,24)(23,25)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19777);