Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#26209 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2414 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G | |
830 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)(16,20)(17,19)(18,21)(22,23)(24,28)(25,26)(27,29)(30,31,35,34)(32,36,39,42)(33,37,41,43)(38,44,45,40);(14,16,17,21)(15,18,19,20)(23,26)(27,28)(30,32)(31,36)(33,40)(34,42)(35,39)(37,38)(41,44)(43,45);(22,24,25,29)(23,27,26,28)(30,33,35,41)(31,37,34,43)(32,38,39,45)(36,44,42,40);(15,19)(18,20)(23,26)(27,28)(30,31,35,34)(32,36,39,42)(33,37,41,43)(38,44,45,40)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19197);