Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C9 · Schur multiplier (H2) = C37 |
| direct product | C2×C32×C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C34 | C32 |
| commutator | C3 | C2×C33×C9 |
| Frattini, cosocle | C32 | C2×C34 |
| prime radical | C2×C35 | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C34 ◁ G | |
2996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 486 |
A minimal faithful permutation representation — 4 generators on 26 points:
(1,2)(3,4,5);(6,7,8);(9,10,12)(11,14,16)(13,17,15)(18,19,21,20,22,24,23,25,26);(10,13,14)(12,16,17)594 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 416);