Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#17351 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×C13×#41 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×D4×C13 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,18,17,19,20,21)(22,23)(24,30,32,27)(25,28)(26,29)(31,36,37,34)(33,35);(22,24,26,32)(23,27,29,30)(25,31,33,37)(28,34,35,36);(22,25)(23,28)(24,31)(26,33)(27,34)(29,35)(30,36)(32,37);(25,33)(28,35)(31,37)(34,36)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10339);