Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C7 · Schur multiplier (H2) = C9 |
| direct product | C7×#6896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C7 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C7 |
| prime radical | C33×C7 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C7 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 567 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4,5,6,7)(9,13,15)(10,14,16)(18,19,23)(21,24,22);(8,9,14,12,15,16,11,13,10)(17,18,21,20,19,22,25,23,24);(8,10,13,11,16,15,12,14,9)(17,19,24,20,23,21,25,18,22)357 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 43);