Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#106 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C24×C13 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,25,23,28,35,27)(20,29,32,46,33,47,30,44)(22,36,34,26,38,43,48,45)(24,39,41,31,42,37,40,49);(18,20,23,33)(19,24)(21,30,35,32)(22,37,38,39)(25,40)(26,44)(27,41)(28,42)(29,36)(31,48,49,34)(43,47)(45,46);(15,17)(18,21,23,35)(19,25,28,27)(20,30,33,32)(22,34,38,48)(24,40,42,41)(26,43,45,36)(29,44,47,46)(31,39,49,37)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5918);