Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13068 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1893 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3067 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
456 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)(14,15,19,24,21,17,20,32)(16,25,29,41,30,42,28,40)(18,33,34,31,36,45,35,23)(22,37,39,44,26,43,38,27);(14,16,18,27,19,29,34,37,21,30,36,44,20,28,35,43)(15,22,31,42,32,38,33,41,17,26,23,25,24,39,45,40);(14,17)(15,21)(16,26)(18,23)(19,24)(20,32)(22,30)(25,27)(28,38)(29,39)(31,36)(33,35)(34,45)(37,40)(41,43)(42,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6058);