Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61933 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3508 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,21)(18,22)(19,23)(20,26)(25,29)(27,28)(30,31,35,40)(32,42,33,37)(34,41,36,39)(38,43,45,44);(14,16,19,26)(15,20,23,24)(17,25,18,27)(21,28,22,29)(30,32,35,33)(31,37,40,42)(34,44,36,43)(38,41,45,39);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,24,29)(30,33,35,32)(31,38,40,45)(34,44,36,43)(37,41,42,39);(14,18,19,17)(15,22,23,21)(16,25,26,27)(20,28,24,29);(15,23)(20,24)(21,22)(28,29)(30,34,35,36)(31,39,40,41)(32,43,33,44)(37,45,42,38)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54921);