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×#9792 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #390 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19,18,22,25,21)(16,23,26,20,24,27,29,28)(30,31,34,37,33,36,38,44)(32,35,40,43,39,42,41,45);(15,19,22,21)(16,24)(20,23,28,27)(26,29)(30,32,38,40,33,39,34,41)(31,35,37,45,36,42,44,43);(14,16,25,29,18,24,17,26)(15,20,19,27,22,28,21,23)(31,36)(32,39)(37,44)(40,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2780);