Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23875 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1642 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)(16,26)(17,22)(18,31)(19,34)(20,25)(21,28)(23,32)(24,36)(27,37)(29,45)(30,38)(33,41)(35,40)(39,44)(42,43);(14,16,20,17)(15,21,25,38)(18,27,33,29)(19,30,36,28)(22,34,26,24)(23,37,40,45)(31,42,41,39)(32,44,35,43);(14,17,20,16)(15,22,25,26)(18,29,33,27)(19,28,36,30)(21,24,38,34)(23,39,40,42)(31,37,41,45)(32,43,35,44);(14,18)(15,23)(16,27)(17,29)(19,35)(20,33)(21,37)(22,39)(24,41)(25,40)(26,42)(28,44)(30,43)(31,34)(32,36)(38,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16863);