Finite Group DatabasebetaFinite Group Databasebeta| order | 36224 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C26×D283 |
| unambiguous semidirect product | C283⋊C27 |
| unambiguous semidirect product | (C2×C283)⋊C26 |
| Fitting, socle | C26×C283 ⋊ C2 |
| derived, Sylow | C283 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D283 |
| commutator, cosocle, hypocenter | C283 | C27 |
| Frattini | C1 | G |
| Fitting, socle | C26×C283 | C2 |
| LCS | G ▷ C283 | |
| UCS | C1 ◁ C26 | |
58424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18112 |
9152 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36224, 19324);