Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#8817 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #127 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,26)(21,30)(22,24)(23,28)(25,27)(29,32)(31,33)(34,35)(36,42)(37,39)(38,46)(40,44)(41,45)(43,48)(47,49);(18,20,27,33,22,29,21,28)(19,23,30,32,24,31,25,26)(35,39)(40,47)(41,46)(42,48);(19,24)(23,31)(25,30)(26,32)(34,36,38,44,37,43,45,49)(35,40,41,42,39,47,46,48)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1805);