Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624932 ⋊ C2 |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|c^3=g^2,d^a=d^2,e^a=e^2g^2,c^b=cf,f^b=fg,e^d=eg78 conjugacy classes — view the full character table.
| maximal subgroup of | #72243714, #72243731, #72243736, … |
| maximal normal subgroup of | #72243714, #72243731, #72243736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1727);