Finite Group DatabasebetaFinite Group Databasebeta| order | 36004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C9001 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C9001 | C4 |
| prime radical, cosocle | D9001 | C2 |
| LCS | G ▷ C9001 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9001 |
Polycyclic presentation:
2^2,9001|a^2=b,c^a=c^1237,c^b=c^90002254 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36004, 3);