Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10902 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #385 |
| prime radical | C24×C13 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
670 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,22,28,24,29,23,27)(20,30,33,41,34,40,32,25)(21,35,36,43,38,42,37,26)(31,45,47,49,48,39,46,44);(18,20,23,32,24,34,22,33)(19,25,27,40,29,41,28,30)(21,31,37,46,38,48,36,47)(26,39,42,49,43,45,35,44);(14,16,17,15)(18,21,22,36,24,38,23,37)(19,26,28,35,29,43,27,42)(20,31,33,47,34,48,32,46)(25,39,30,44,41,45,40,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3890);