Finite Group DatabasebetaFinite Group Databasebeta| order | 2187 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #14552178 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C37 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C33 | C34 |
| prime radical | C3×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
1922 conjugacy classes of subgroups; only the 332 normal subgroups are shown.
This group has 1922 conjugacy classes of subgroups — too many to draw. Only its 332 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
3^7|b^3=f,c^3=f,b^a=be,c^b=cf,d^c=dg219 conjugacy classes — view the full character table.
| Fitting subgroup of | #72243418, #72243510, #72269289 |
| maximal subgroup of | #72243407, #72243418, #72243510 |
| maximal normal subgroup of | #72243407, #72243418, #72243510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2187, 6041);