Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13215 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#13215 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1961 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
466 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)(17,32,36,41)(18,30)(19,24)(20,26)(21,25)(22,35,40,38)(23,28)(29,34,39,44)(31,37)(33,42,45,43);(14,16,28,26,19,31,37,24,20,23,27,15,21,30,18,25)(17,33,42,41,35,39,34,40,36,45,43,32,38,29,44,22);(14,17,20,36)(15,22)(16,29)(18,34,37,44)(19,35,21,38)(23,39)(24,32)(25,41)(26,40)(27,42,28,43)(30,45)(31,33)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6203);