Finite Group DatabasebetaFinite Group Databasebeta| order | 30954 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C67⋊C3)⋊C11)⋊D7 |
| unambiguous semidirect product | ((C67⋊C3)⋊D7)⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C67 | C2×C3×C11 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 469 |
Polycyclic presentation:
2,3,7,11,67|c^a=c^6,e^a=e^66,e^b=e^37,e^d=e^64172 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30954, 69);