Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12986 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #386 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1869 |
| prime radical | C2×C13×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C8×C13 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25,19,24,38,42,21,26,40,44,18,37,28,29)(16,27,31,45,32,17,34,36,33,35,23,43,30,22,41,39);(14,16,28,41,18,30,40,23,21,33,38,34,19,32,20,31)(15,22,42,45,37,35,25,39,26,17,29,43,24,27,44,36);(14,17)(15,23)(16,29)(18,27)(19,35)(20,39)(21,22)(24,41)(25,32)(26,31)(28,43)(30,44)(33,42)(34,37)(36,40)(38,45)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5974);