Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34530 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,24)(21,28)(22,23)(25,29)(26,32)(27,30)(31,33)(34,35,39,42)(36,37,44,40)(38,46,47,41)(43,48,49,45);(19,23)(24,30)(25,28)(31,32)(34,36,39,44)(35,40,42,37)(38,43,47,49)(41,48,46,45);(14,15,17,16)(18,20,22,27)(19,24,23,30)(21,26,29,33)(25,31,28,32)(34,36)(35,40)(37,42)(38,43)(39,44)(41,48)(45,46)(47,49);(18,19)(20,24)(21,25)(22,23)(26,31)(27,30)(28,29)(32,33)(34,37,39,40)(35,36,42,44)(38,45,47,48)(41,43,46,49);(14,16,17,15)(18,21)(19,25)(20,26)(22,29)(23,28)(24,31)(27,33)(30,32)(34,38,39,47)(35,41,42,46)(36,43,44,49)(37,45,40,48)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27518);