Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #14555436 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C310 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3 | C33×H(3,𝔽3) |
| commutator, Frattini, cosocle | C32 | C35 |
| prime radical | C3×H(5,𝔽3) | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ C32×H(3,𝔽3) ◁ G | |
| LECS | G ▷ C32 ▷ C3 ▷ C1 | |
6164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|b^3=g,b^a=bf,f^a=fg,e^b=eg,d^c=dg299 conjugacy classes — view the full character table.
| Fitting subgroup of | #72243624, #72243637, #72243729, … |
| maximal subgroup of | #72221882, #72221888, #72221916, … |
| maximal normal subgroup of | #72221882, #72221888, #72221916, … |
| maximal quotient of | C2×#14555437 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 9296);