Finite Group DatabasebetaFinite Group Databasebeta| order | 21070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×C5⋊(D43⋊C7) |
| unambiguous semidirect product | C5⋊(C7×D43⋊C7) |
| unambiguous semidirect product | (C43⋊C7)⋊(C7×D5) |
| unambiguous semidirect product | D215⋊C72 |
| unambiguous semidirect product | (C7×D215)⋊C7 |
| Fitting, socle | C5×C7×C43 ⋊ C2×C7 |
| derived, Hall | C5×C43 ⋊ C2×C72 |
| Hall | C5×C7×C43⋊C7 ⋊ C2 |
| Hall | C7×C43⋊C7 ⋊ D5 |
| Hall | D215 ⋊ C72 |
| Sylow | C43 ⋊ C72×D5 |
| Sylow | C5 ⋊ C7×D43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C5⋊(D43⋊C7) |
| commutator, cosocle, hypocenter | C5×C43 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C43 | C2×C7 |
| LCS | G ▷ C5×C43 | |
| UCS | C1 ◁ C7 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1505 |
301 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21070, 17);