Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#9790 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #390 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C22×D4×C13 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,22,19,23,17,20)(16,24,27,29,25,28,26,21)(30,31,33,37,34,36,41,42)(32,35,39,44,38,43,40,45);(15,20,23,22)(16,25)(21,24,29,28)(26,27)(30,32,33,40,34,38,41,39)(31,35,42,44,36,43,37,45);(14,16,17,26,19,25,18,27)(15,21,22,24,23,29,20,28)(32,38)(35,43)(39,40)(44,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2778);