Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C22×#731 ⋊ C3 |
| Sylow | C22 ⋊ #6913 |
140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^5,2^2|a^3=e,c^3=e,c^a=ce,f^a=fg,g^a=f,c^b=cd,d^b=de52 conjugacy classes — view the full character table.
| maximal subgroup of | #11757803⋊C2, C2×#11757803 |
| maximal normal subgroup of | #11757803⋊C2, C2×#11757803 |
| maximal quotient of | #14517210, C2×#11757803 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 528);