Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19863 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3303 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(17,25)(20,26)(21,22)(23,29)(27,28)(30,31,35,38)(32,36,34,42)(33,40,41,44)(37,43,45,39);(14,15,18,22)(16,20,24,28)(17,21,25,19)(23,27,29,26)(30,32,35,34)(31,36,38,42)(33,39,41,43)(37,44,45,40);(14,16,18,24)(15,20,22,28)(17,23,25,29)(19,26,21,27)(30,33)(31,37)(32,39)(34,43)(35,41)(36,44)(38,45)(40,42);(15,21)(17,25)(19,22)(20,27)(23,29)(26,28)(30,32,35,34)(31,36,38,42)(33,39,41,43)(37,44,45,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12851);