Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624900 ⋊ C2 |
331 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^6|b^3=g,d^3=f,b^a=b^2eg^2,g^a=g^2,c^b=cf,d^b=dg,e^c=ef110 conjugacy classes — view the full character table.
| maximal subgroup of | #72221845, #72221864, #72243254, … |
| maximal normal subgroup of | #72221864, #72243254, C2×#13091525 |
| maximal quotient of | #72221846, #72243243, #72243546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1599);