Finite Group DatabasebetaFinite Group Databasebeta| order | 36924 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#10624382⋊C3 |
| unambiguous semidirect product | #10624382⋊(C3×C17) |
| unambiguous semidirect product | (C17×#10624382)⋊C3 |
| Fitting, socle, Hall | C17×C181 ⋊ C3×C4 |
| derived, Sylow | C181 ⋊ C3×C4×C17 |
| Hall | C17×#10624382 ⋊ C3 |
| Hall | C17×C181⋊C3 ⋊ C4 |
| Hall | #10624382 ⋊ C3×C17 |
| Hall | C181⋊C3 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #10624382⋊C3 |
| commutator, hypocenter | C181 | C3×C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C181 | C3×C4 |
| prime radical | C17×D181⋊C3 | C2 |
| cosocle | D181 | C2×C3×C17 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3077 |
459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36924, 14);