Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C7 |
| direct product | C11⋊C5×C5⋊(C7⋊D7) |
| unambiguous semidirect product | C5⋊(C11⋊C5×C7⋊D7) |
| unambiguous semidirect product | C7⋊(C11⋊C5×D35) |
| unambiguous semidirect product | (C11×C5⋊(C7⋊D7))⋊C5 |
| Fitting, socle, derived | C5×C72×C11 ⋊ C2×C5 |
| Hall | C5×C72×C11⋊C5 ⋊ C2 |
| Hall | C72×C11 ⋊ C5×D5 |
| Hall | C5×C11⋊C5 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D5×C11⋊C5 |
| Sylow | C11 ⋊ C5×C5⋊(C7⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C11 | C2×C5 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2695 |
868 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 62);