Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15668527⋊C9 |
| derived, Hall | C52×C29 ⋊ C4×C9 |
| Hall | C29×C52⋊C9 ⋊ C4 |
| Hall | #15668527 ⋊ C9 |
| Hall | C52⋊C9 ⋊ Dic29 |
| Sylow | C29 ⋊ #1043⋊C9 |
| Sylow | C52 ⋊ C9×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #15668527⋊C3 |
| commutator, hypocenter | C52×C29 | C4×C9 |
| Fitting, socle | C3×C52×C29 | C3×C4 |
| prime radical, cosocle | C3×C29×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C29 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
Polycyclic presentation:
2,3,2,5^2,29,3|a^2=c,b^3=g,d^a=d^3,e^a=e^3,f^a=f^28,d^b=d^3e^3,e^b=d^4e,d^c=d^4,e^c=e^4462 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 140);