Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#29153 |
| 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 ◁ C13×#376 ◁ G | |
686 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)(14,15,18,21)(16,20,17,19)(22,23,25,27)(24,26,28,29)(30,31,35,42,34,38,33,37)(32,36,43,45,40,39,41,44);(14,16,18,17)(15,19,21,20)(22,24,25,28)(23,26,27,29)(30,32)(31,36)(33,41)(34,40)(35,43)(37,44)(38,39)(42,45);(24,28)(26,29)(30,31,34,38)(32,39,40,36)(33,42,35,37)(41,44,43,45);(14,17,18,16)(15,20,21,19)(32,40)(36,39)(41,43)(44,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 22141);