Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C24×C13 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1898 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)(18,19,23,21)(20,24,28,26)(22,29,30,25)(27,32,33,31)(35,39)(36,42)(37,45)(47,49);(19,21)(24,26)(25,29)(31,32)(34,35,38,39)(36,43,42,40)(37,41,45,46)(44,49,48,47);(18,20,23,28)(19,24,21,26)(22,27,30,33)(25,31,29,32)(34,35)(36,40)(37,41)(38,39)(42,43)(44,47)(45,46)(48,49);(18,21,23,19)(20,26,28,24)(22,29,30,25)(27,32,33,31)(34,36,38,42)(35,40,39,43)(37,44,45,48)(41,47,46,49);(18,22,23,30)(19,25,21,29)(20,27,28,33)(24,31,26,32)(34,37,38,45)(35,41,39,46)(36,44,42,48)(40,47,43,49)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27363);