Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1990 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(19,23)(20,26)(25,30)(27,32)(34,35)(36,39)(37,42)(38,43)(40,44)(41,46)(45,47)(48,49);(19,23)(24,29)(25,30)(31,33)(35,36)(37,44)(41,43)(45,49);(18,19)(20,24)(21,25)(22,23)(26,29)(27,31)(28,30)(32,33)(34,36,39,35)(37,42,44,40)(38,43,46,41)(45,48,49,47);(18,20,22,26)(19,24,23,29)(21,27,28,32)(25,31,30,33)(34,37)(35,40)(36,42)(38,45)(39,44)(41,47)(43,48)(46,49);(18,21,22,28)(19,25,23,30)(20,27,26,32)(24,31,29,33)(34,38)(35,41)(36,43)(37,45)(39,46)(40,47)(42,48)(44,49)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27393);