Finite Group DatabasebetaFinite Group Databasebeta| order | 24492 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic157⋊C3)⋊C13 |
| unambiguous semidirect product | (Dic157⋊C13)⋊C3 |
| derived, Sylow | C157 ⋊ C3×C4×C13 |
| Hall | Dic157⋊C13 ⋊ C3 |
| Hall | (C157⋊C3)⋊C13 ⋊ C4 |
| Hall | C157⋊C13 ⋊ C3×C4 |
| Hall | Dic157⋊C3 ⋊ C13 |
| Hall | Dic157 ⋊ C3×C13 |
| Hall | C157⋊C3 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (D157⋊C3)⋊C13 |
| commutator, hypocenter | C157 | C3×C4×C13 |
| Fitting, socle, cosocle | C2×C157 | C2×C3×C13 |
| prime radical | C2×(C157⋊C3)⋊C13 | C2 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,157,2|a^2=e,d^a=d^156,d^b=d^12,d^c=d^130160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24492, 30);