Finite Group DatabasebetaFinite Group Databasebeta| order | 36324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1009 ⋊ C4×C9 |
| Hall | #22583792 ⋊ C4 |
| Hall | Dic1009 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D1009⋊C3 |
| commutator, hypocenter | C1009 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C1009 | C2×C3 |
| LCS | G ▷ C1009 | |
| UCS | C1 ◁ C2×C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36324 |
Polycyclic presentation:
2,3,1009,2,3|a^2=d,b^3=e,c^a=c^1008,c^b=c^3741044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36324, 2);