Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#12881 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | #432 |
| prime radical | C23×C13 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
298 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)(15,16)(18,19,22,29,23,26,38,42,24,27,37,43,21,28,35,44)(20,30,32,45,33,40,47,49,34,25,36,41,31,39,46,48);(14,15,17,16)(18,20,21,31,24,34,23,33)(19,25,28,40,27,30,26,39)(22,36,35,47,37,32,38,46)(29,45,44,48,43,41,42,49);(14,16,17,15)(19,26,27,28)(22,37)(25,39,30,40)(29,44,43,42)(32,36)(35,38)(41,49,45,48)(46,47)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5869);