Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #14550934 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3 | #10624596 |
| commutator, Frattini, cosocle | C34 | C33 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ C33 ◁ C32×H(3,𝔽3) ◁ G | |
| LECS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
419 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 419 conjugacy classes of subgroups — too many to draw. Only its 44 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=ef,b^a=bd,c^a=ce,d^a=de,e^a=eg,f^a=fg^2,d^b=df,e^b=eg^2,d^c=dg^275 conjugacy classes — view the full character table.
| maximal subgroup of | #72265150, #72265284, #72265346, … |
| maximal normal subgroup of | #72265150, #72265284, #72265346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4793);