Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19123 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×#121 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
628 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)(18,27)(19,22)(20,25)(24,28)(26,29)(30,31)(32,38)(33,35)(34,42)(36,40)(37,41)(39,45)(43,44);(14,16,18,25,19,26,17,24)(15,20,21,23,22,28,27,29)(31,35)(36,44)(37,42)(38,45);(30,32,33,39)(31,36,35,44)(34,43,41,40)(37,45,42,38);(14,17,19,18)(15,21,22,27)(16,24,26,25)(20,23,28,29)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12111);