Finite Group DatabasebetaFinite Group Databasebeta| order | 36372 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic433⋊C3 |
| unambiguous semidirect product | Dic433⋊(C3×C7) |
| derived, Sylow | C433 ⋊ C3×C4×C7 |
| Hall | C7×Dic433 ⋊ C3 |
| Hall | C7×C433⋊C3 ⋊ C4 |
| Hall | C7×C433 ⋊ C3×C4 |
| Hall | Dic433 ⋊ C3×C7 |
| Hall | C433⋊C3 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D433⋊C3 |
| commutator, hypocenter | C433 | C3×C4×C7 |
| Frattini | C2 | C7×D433⋊C3 |
| Fitting, socle | C2×C7×C433 | C2×C3 |
| prime radical | C2×C7×C433⋊C3 | C2 |
| cosocle | C2×C433 | C2×C3×C7 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12124 |
1092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36372, 13);