Finite Group DatabasebetaFinite Group Databasebeta| order | 30954 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×D7×C67⋊C11 |
| unambiguous semidirect product | (C3×D7×C67)⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×C67⋊C11 |
| commutator, cosocle, hypocenter | C7×C67 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C67 | C2×C11 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1407 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30954, 27);