Finite Group DatabasebetaFinite Group Databasebeta| order | 30124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic443⋊C17 |
| unambiguous semidirect product | (C443⋊C17)⋊C4 |
| derived, Sylow | C443 ⋊ C4×C17 |
| Hall | C443⋊C17 ⋊ C4 |
| Hall | Dic443 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D443⋊C17 |
| commutator, hypocenter | C443 | C4×C17 |
| Fitting, socle, cosocle | C2×C443 | C2×C17 |
| prime radical | C2×C443⋊C17 | C2 |
| LCS | G ▷ C443 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1772 |
Polycyclic presentation:
2,17,443,2|a^2=d,c^a=c^442,c^b=c^12394 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30124, 2);