Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33457 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
682 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,28)(21,32)(22,37)(23,25)(24,29)(26,35)(27,34)(30,48)(31,45)(33,43)(36,44)(38,42)(39,47)(40,49)(41,46);(18,20,23,31)(19,24,25,39)(21,33,36,49)(22,38,34,30)(26,42,41,48)(27,43,37,40)(28,44,45,32)(29,46,47,35);(14,16,17,15)(18,19)(20,24)(21,26)(22,27)(23,25)(28,29)(30,40)(31,39)(32,35)(33,42)(34,37)(36,41)(38,43)(44,46)(45,47)(48,49);(19,25)(24,39)(26,41)(27,37)(28,45)(32,44)(40,43)(42,48)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26445);