Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13190 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C23 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C23×C13 | C22×C8 |
| prime radical | C22×D4×C13 | C8 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,21)(22,23,27,31,28,30,35,36,26,24,29,33,25,32,34,37);(14,15,16,17)(22,24,27,33,28,32,35,37,26,23,29,31,25,30,34,36);(18,19,20,21)(22,25,26,28)(23,30,24,32)(27,34,29,35)(31,36,33,37)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6178);