Finite Group DatabasebetaFinite Group Databasebeta| order | 4401 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C163 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C163 | C27 |
| prime radical | C163⋊C3 | C9 |
| cosocle | #13091814 | C3 |
| LCS | G ▷ C163 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 163 |
| transitive degree | μt(G) = 163 |
Polycyclic presentation:
3^3,163|a^3=b,b^3=c,d^a=d^64,d^b=d^40,d^c=d^10433 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#17984252, #27210147, #72215751 |
| maximal normal subgroup of | C3×#17984252, #27210147, #72215751 |
| maximal quotient of | #27210145, C3×#17984252 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4401, 16);