Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting, Sylow | #10624930 ⋊ C2 |
446 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 27 |
Polycyclic presentation:
2,3^6|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 | #72243618, #72243636, #72243647, … |
| maximal normal subgroup of | #72243618, #72243636, #72243647, … |
| maximal quotient of | C3×#13091643 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1717);