Finite Group DatabasebetaFinite Group Databasebeta| order | 16775 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C11×C61 ⋊ C25 |
| Sylow | C61 ⋊ C11⋊C25 |
| Sylow | C11 ⋊ C61⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #16809824 |
| commutator, hypocenter | C11×C61 | C25 |
| Fitting, socle, prime radical, cosocle | C5×C11×C61 | C5 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16775 |
Polycyclic presentation:
5,11,61,5|a^5=d,b^a=b^4,c^a=c^9695 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30680844, #46776657, #46776663, … |
| maximal normal subgroup of | C2×#30680844, #46776657, #46776663, … |
| maximal quotient of | C2×#30680844 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16775, 7);