Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12662 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C22 | C2×C4×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle, prime radical | C23×C13 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(22,23,26,30,27,31,35,37,25,28,32,36,34,24,29,33);(15,17)(18,19,20,21)(23,28)(24,31)(30,36)(33,37);(22,24,32,37,27,23,29,36,25,31,26,33,34,28,35,30)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5650);