Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#23847 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #401 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| socle | C2×C13 | C2×#401 |
| prime radical | C24×C13 | C24 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
604 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)(16,24,27,20)(17,21,30,36)(18,22)(19,23)(25,34)(26,38,40,33)(28,32)(29,35,42,45)(31,37)(39,44)(41,43);(14,16)(15,20)(17,28,30,25)(18,26)(19,27)(21,34,36,32)(22,33)(23,24)(29,41,42,39)(31,40)(35,44,45,43)(37,38);(14,17)(15,21,23,36)(16,25)(18,29)(19,30)(20,32,24,34)(22,35,37,45)(26,39)(27,28)(31,42)(33,43,38,44)(40,41);(14,18,19,31)(15,22,23,37)(16,26,27,40)(17,29,30,42)(20,33,24,38)(21,35,36,45)(25,39,28,41)(32,43,34,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16835);