Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34505 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1932 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)(14,15,17,16)(19,23)(20,26)(25,30)(27,32)(34,35,40,38)(36,43,37,41)(39,46,47,42)(44,48,45,49);(19,23)(24,29)(25,30)(31,33)(34,36,40,37)(35,41,38,43)(39,44,47,45)(42,48,46,49);(18,19)(20,24)(21,25)(22,23)(26,29)(27,31)(28,30)(32,33)(34,37,40,36)(35,41,38,43)(39,45,47,44)(42,48,46,49);(14,16,17,15)(18,20)(19,24)(21,27)(22,26)(23,29)(25,31)(28,32)(30,33)(34,38,40,35)(36,41,37,43)(39,46,47,42)(44,48,45,49);(18,21,22,28)(19,25,23,30)(20,27,26,32)(24,31,29,33)(34,39,40,47)(35,42,38,46)(36,44,37,45)(41,48,43,49)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27493);