Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C29×C52⋊C9 ⋊ C4 |
| Hall | C52×C29 ⋊ Dic9 |
| Hall | C52⋊C9 ⋊ #1181 |
| Sylow | C29 ⋊ #11744607 |
| Sylow | C52 ⋊ C9⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C29×C52⋊C9 | C4 |
| Frattini | C3 | #22576417 |
| Fitting, socle | C3×C52×C29 | Dic3 |
| prime radical | C3×C52×D29 | D3 |
| cosocle | D29×C52⋊C9 | C2 |
| LCS | G ▷ C29×C52⋊C9 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1305 |
Polycyclic presentation:
2^2,3,29,5^2,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^17,e^a=e^2f,f^a=e^2f^3,g^a=g^2,d^b=d^28,e^c=e^2f^4,f^c=e^2f^2279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 135);