Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C7 |
| 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 ⋊ C5⋊AGL(1,𝔽11) |
| 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 |
Polycyclic presentation:
2,5^2,7^2,11|c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^10,f^b=f^4865 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 61);