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×#19828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3305 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
614 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)(14,15,18,22)(16,20,24,28)(17,19,25,21)(23,29,26,27)(30,31)(32,36)(33,40)(34,42)(35,38)(37,39)(41,44)(43,45);(15,19)(16,23)(17,25)(20,28)(21,22)(24,26)(30,32,35,34)(31,36,38,42)(33,39,41,43)(37,44,45,40);(30,33,35,41)(31,37,38,45)(32,39,34,43)(36,44,42,40);(14,16,18,24)(15,20,22,28)(17,26,25,23)(19,27,21,29)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12816);