Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#20512 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C4 | C22×C42×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,22,26,23,20,27,25)(21,24,30,32,29,28,33,31);(14,15,17,16)(18,20)(19,23)(21,28)(22,25)(24,29)(26,27)(30,31)(32,33);(14,16,17,15)(21,29)(24,28)(30,33)(31,32);(18,21,22,30,23,29,27,33)(19,24,26,32,20,28,25,31)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13500);