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×#19858 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#459 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
580 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)(15,20)(16,18)(21,28)(22,26)(23,27)(24,29)(30,31)(32,36)(33,40)(34,42)(35,38)(37,39)(41,44)(43,45);(14,15,19,22)(16,20,18,26)(17,24,25,28)(21,27,29,23)(30,32,35,34)(31,36,38,42)(33,39,41,43)(37,44,45,40);(14,16,19,18)(15,20,22,26)(17,23,25,27)(21,28,29,24)(30,33)(31,37)(32,39)(34,43)(35,41)(36,44)(38,45)(40,42);(14,17,19,25)(15,21,22,29)(16,23,18,27)(20,28,26,24)(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, 12846);