Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #14550628 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C310 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3 | #10624562 |
| commutator, Frattini, cosocle | C34 | C33 |
| LCS | G ▷ C34 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3 ◁ C34 ◁ G | |
| LECS | G ▷ C34 ▷ C3 ▷ C1 | |
1994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
3^7|b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg^2,d^c=dg107 conjugacy classes — view the full character table.
| maximal subgroup of | #72264976, #72265289, #72265348 |
| maximal normal subgroup of | #72264976, #72265289, #72265348 |
| maximal quotient of | #72265407, #72265412 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 4487);