Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24000 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3019 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,27)(18,31)(19,23)(21,30)(22,33)(24,39)(25,41)(26,36)(28,44)(29,38)(32,37)(34,40)(35,43)(42,45);(14,16,19,26)(15,20,23,36)(17,28)(18,25,33,43)(21,34)(22,35,31,41)(24,29)(27,39)(30,42)(32,40)(37,45)(38,44);(14,17)(15,21)(16,24)(18,32)(19,29)(20,34)(22,38)(23,37)(25,42)(26,28)(27,31)(30,33)(35,44)(36,45)(39,41)(40,43);(18,33)(22,31)(25,43)(27,38)(30,32)(35,41)(39,44)(40,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16988);