Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13337 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
554 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(19,26)(20,32)(21,37)(22,40)(23,24)(27,44)(28,31)(29,38)(30,41)(34,42)(35,39)(36,48)(43,45)(47,49);(14,15)(16,17)(18,19,25,31)(20,33,36,46)(21,38,22,41)(23,30,24,29)(26,40,28,37)(27,35,44,34)(32,45,48,49)(39,47,42,43);(15,17)(18,20)(19,27)(21,39)(22,42)(23,35)(24,34)(25,36)(26,43)(28,47)(29,46)(30,33)(31,44)(32,40)(37,48)(38,49)(41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6325);