Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#17925 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C13×#431 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,21,18,20,24,27)(16,19,22,26,23,25,28,29)(30,31,35,38,36,32,34,40)(33,37,43,44,41,39,42,45);(30,32,36,31)(33,39,41,37)(34,38,35,40)(42,44,43,45);(14,16,17,22,18,23,24,28)(15,19,21,26,20,25,27,29)(30,33,34,42,36,41,35,43)(31,37,40,45,32,39,38,44);(15,20)(19,25)(21,27)(26,29)(33,41)(37,39)(42,43)(44,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10913);