Finite Group DatabasebetaFinite Group Databasebeta| order | 30124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D443 |
| unambiguous semidirect product | (D17×C443)⋊C2 |
| unambiguous semidirect product | (C17×D443)⋊C2 |
| unambiguous semidirect product | D7531⋊C2 |
| Fitting, socle, derived, Hall | C17×C443 ⋊ C22 |
| Sylow | C443 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D443 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C443 | C22 |
| LCS | G ▷ C17×C443 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7531 |
2230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30124, 12);