Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#32837 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,18,20,21)(30,31)(32,36)(33,37)(34,35)(38,44)(39,42)(40,43)(41,45);(14,16)(15,18)(17,20)(19,21)(22,23,25,28)(24,26,29,27)(31,35)(33,40)(36,42)(38,41);(15,19)(18,21)(23,26)(24,29)(27,28)(30,32,34,39)(31,36,35,42)(33,41,40,38)(37,45,43,44);(16,20)(18,21)(30,33,34,40)(31,37,35,43)(32,38,39,41)(36,44,42,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25825);