Finite Group DatabasebetaFinite Group Databasebeta| order | 26700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #22581840⋊C3 |
| Fitting, socle, derived, Hall | C52×C89 ⋊ C3×C4 |
| Hall | #22581840 ⋊ C3 |
| Hall | C52⋊C3×C89 ⋊ C4 |
| Sylow | C89 ⋊ #1039⋊C3 |
| Hall | C52⋊C3 ⋊ #67063 |
| Sylow | C52 ⋊ C3×#67063 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C89 | C3×C4 |
| prime radical | C52⋊C3×D89 | C2 |
| cosocle | C52×D89 | C2×C3 |
| LCS | G ▷ C52×C89 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1335 |
Polycyclic presentation:
2,3,2,5^2,89|a^2=c,d^a=d^4,e^a=e^4,f^a=f^55,d^b=de,e^b=d^2e^3,f^c=f^88262 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26700, 59);