Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34403 |
| 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)(19,23)(20,26)(25,30)(27,32)(34,35)(36,43)(37,40)(38,46)(39,42)(41,47)(44,48)(45,49);(19,23)(24,29)(25,30)(31,33)(34,36,39,37)(35,40,42,43)(38,44,47,45)(41,48,46,49);(18,19)(20,24)(21,25)(22,23)(26,29)(27,31)(28,30)(32,33)(34,37,39,36)(35,40,42,43)(38,45,47,44)(41,48,46,49);(18,20,22,26)(19,24,23,29)(21,27,28,32)(25,31,30,33)(34,35)(36,43)(37,40)(38,41)(39,42)(44,49)(45,48)(46,47);(18,21,22,28)(19,25,23,30)(20,27,26,32)(24,31,29,33)(34,38,39,47)(35,41,42,46)(36,44,37,45)(40,48,43,49)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27391);