Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#32725 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G | |
750 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)(14,15,17,20)(16,19,21,18)(22,23)(24,26)(25,27)(28,29);(14,16)(15,18)(17,21)(19,20)(22,24)(23,26)(25,28)(27,29)(30,31,35,38)(32,39,41,44)(33,37,34,42)(36,43,45,40);(14,16)(15,19)(17,21)(18,20)(23,27)(26,29)(30,32,35,41)(31,36,38,45)(33,40,34,43)(37,44,42,39);(16,21)(18,19)(24,28)(26,29)(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25713);