Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18682 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18711 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
818 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)(16,23)(17,21)(18,26)(19,22)(20,24)(25,28)(27,29)(30,31,36,41)(32,42,38,45)(33,44,37,43)(34,39,35,40);(14,15)(16,20)(17,21)(18,26)(19,22)(23,27)(24,28)(25,29)(30,32,36,38)(31,37,41,33)(34,43,35,44)(39,42,40,45);(14,16)(15,20)(17,24)(18,27)(19,25)(21,28)(22,29)(23,26)(30,33,36,37)(31,38,41,32)(34,42,35,45)(39,43,40,44);(14,17,19,18)(15,21,22,26)(16,24,25,27)(20,28,29,23)(30,34,36,35)(31,39,41,40)(32,43,38,44)(33,45,37,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11699);