Finite Group DatabasebetaFinite Group Databasebeta| order | 18775 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C751 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C751 | C25 |
| prime radical, cosocle | C751⋊C5 | C5 |
| LCS | G ▷ C751 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 751 |
Polycyclic presentation:
5^2,751|a^5=b,c^a=c^481,c^b=c^8055 conjugacy classes — view the full character table.
| maximal subgroup of | #34037397⋊C2, C2×#34037397 |
| maximal normal subgroup of | #34037397⋊C2, C2×#34037397 |
| maximal quotient of | C2×#34037397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18775, 3);