Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13334 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13334 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2011 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,27)(17,21)(18,34)(19,37)(20,25)(22,28)(23,31)(24,35)(26,33)(29,42)(30,39)(32,41)(36,44)(38,43)(40,45);(15,21)(17,31)(18,35)(19,33)(22,27)(23,26)(24,37)(25,34)(28,36)(29,38)(32,45)(39,40)(41,42)(43,44);(14,16)(15,22)(17,32)(18,36)(19,38)(20,30)(21,39)(23,42)(24,43)(25,40)(26,44)(27,34)(28,35)(29,33)(31,45)(37,41)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6322);