Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13161 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | C2×D4 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C8×D4 |
| prime radical | C23×C13 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C22×C13×C16 ◁ 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)(14,15)(16,17)(18,19,23,29,24,28,38,44,25,30,37,27,22,39,21,36)(20,26,33,42,34,41,47,49,35,43,46,40,32,48,31,45);(15,17)(18,20,23,33,24,34,38,47,25,35,37,46,22,32,21,31)(19,26,29,42,28,41,44,49,30,43,27,40,39,48,36,45);(18,21,22,37,25,38,24,23)(19,27,28,36,30,29,39,44)(20,31,32,46,35,47,34,33)(26,40,41,45,43,42,48,49)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6149);