Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13103 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1898 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C13×#3010 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×2−1+4 ◁ G | |
646 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)(14,15,20,25,21,26,19,24)(16,18,23,36,29,37,38,27)(17,30,33,22,34,40,32,41)(28,43,39,31,44,45,42,35);(14,16,27,15)(17,28,43,22)(18,25,19,38)(20,23,37,24)(21,29,36,26)(30,33,39,35)(31,40,32,42)(34,44,45,41);(14,17,21,34)(15,22,26,41)(16,28,29,44)(18,35,37,31)(19,33,20,32)(23,42,38,39)(24,40,25,30)(27,43,36,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6091);