Finite Group DatabasebetaFinite Group Databasebeta| order | 30636 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C23 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C23×C37 ⋊ C3×C4 |
| derived, Sylow | C37 ⋊ C32×C4×C23 |
| Hall | C3×C23×C37⋊C3 ⋊ C4 |
| Hall | C23×#3866 ⋊ C32 |
| Hall | C23×C37 ⋊ C32×C4 |
| Hall | C3×C37⋊C3 ⋊ C4×C23 |
| Hall | #3866 ⋊ C32×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | #3866⋊C3 |
| commutator, hypocenter | C37 | C32×C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C37 | C3×C4 |
| prime radical | C3×C23×D37⋊C3 | C2 |
| cosocle | D37 | C2×C32×C23 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C23 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2553 |
1035 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30636, 72);