Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5×C7 |
| direct product | C5×C11⋊C5×C7⋊D7 |
| unambiguous semidirect product | C7⋊(C5×D7×C11⋊C5) |
| unambiguous semidirect product | (C11×C7⋊D7)⋊C52 |
| unambiguous semidirect product | (C5×C11×C7⋊D7)⋊C5 |
| Fitting, socle | C5×C72×C11 ⋊ C2×C5 |
| derived, Hall | C72×C11 ⋊ C2×C52 |
| Hall | C5×C72×C11⋊C5 ⋊ C2 |
| Hall | C11×C7⋊D7 ⋊ C52 |
| Sylow | C72 ⋊ C2×C5×C11⋊C5 |
| Sylow | C11 ⋊ C52×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊C5×C7⋊D7 |
| commutator, cosocle, hypocenter | C72×C11 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C2×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C5 | |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2695 |
910 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 56);