Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33382 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
1124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(19,24)(21,31)(22,33)(25,37)(26,41)(27,38)(29,44)(30,43)(32,35)(34,36)(39,48)(40,49)(42,47)(45,46);(18,19,23,27)(20,25,28,39)(21,32,34,41)(22,35,33,26)(24,36,38,31)(29,45,42,49)(30,46,43,40)(37,47,48,44);(18,20)(19,25)(21,29)(22,30)(23,28)(24,37)(26,40)(27,39)(31,44)(32,45)(33,43)(34,42)(35,46)(36,47)(38,48)(41,49);(20,28)(25,39)(29,42)(30,43)(37,48)(40,46)(44,47)(45,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26370);