Finite Group DatabasebetaFinite Group Databasebeta| order | 30956 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D71×D109 |
| unambiguous semidirect product | (C109×D71)⋊C2 |
| unambiguous semidirect product | (C71×D109)⋊C2 |
| unambiguous semidirect product | D7739⋊C2 |
| Fitting, socle, derived, Hall | C71×C109 ⋊ C22 |
| Sylow | C109 ⋊ C2×D71 |
| Sylow | C71 ⋊ C2×D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C71×C109 | C22 |
| LCS | G ▷ C71×C109 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7739 |
2072 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30956, 8);