Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#20998 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #386 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C2×C13 | C2×#386 |
| prime radical | C2×C13×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,24,20,25,18,23)(16,26,29,37,30,36,28,21)(17,31,32,22,34,38,33,39)(27,35,41,44,43,45,42,40);(14,16)(15,21,25,37)(17,27)(18,28)(19,29)(20,30)(22,35,39,45)(23,36,24,26)(31,40,38,44)(32,41)(33,42)(34,43);(14,17)(15,22)(16,27)(18,32)(19,33)(20,34)(21,35)(23,38)(24,31)(25,39)(26,40)(28,41)(29,42)(30,43)(36,44)(37,45);(14,18,20,19)(15,23,25,24)(16,28,30,29)(17,32,34,33)(21,36,37,26)(22,38,39,31)(27,41,43,42)(35,44,45,40)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13986);