Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #14550738 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center | C9 | #6896 |
| commutator, Frattini, cosocle | C32×C9 | C33 |
| socle | C3 | #10624565 |
| prime radical | C34 | 3−1+2 |
| LCS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9 ◁ C32×C9 ◁ G | |
| LECS | G ▷ C32×C9 ▷ C3 ▷ C1 | |
281 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 281 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|a^3=e,b^3=d,d^3=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg^2,c^b=cf,e^b=eg^2123 conjugacy classes — view the full character table.
| maximal subgroup of | #72221818, #72221841, C2×#14550738 |
| maximal normal subgroup of | #72221818, #72221841, C2×#14550738 |
| maximal quotient of | C2×#14550738 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4597);