Finite Group DatabasebetaFinite Group Databasebeta| order | 26970 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×D29×ΓL(1,𝔽32) |
| unambiguous semidirect product | C29⋊(C2×C3×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C3×C31×D29)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D29×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C29×C31 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C31 | C2×C5 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2697 |
528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26970, 21);