Finite Group DatabasebetaFinite Group Databasebeta| order | 26700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊#22581820 |
| derived, Hall | C3×C52×C89 ⋊ C4 |
| Hall | C52×C89 ⋊ Dic3 |
| Hall | C3×C89 ⋊ #1039 |
| Sylow | C89 ⋊ C3⋊#1039 |
| Hall | C3×C52 ⋊ Dic89 |
| Sylow | C52 ⋊ Dic267 |
| Sylow | C3 ⋊ #22581820 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊D445) |
| commutator, hypocenter | C3×C52×C89 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52×C89 | C2 |
| LCS | G ▷ C3×C52×C89 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26700 |
Polycyclic presentation:
2,3,5^2,89,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^886678 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26700, 44);