Finite Group DatabasebetaFinite Group Databasebeta| order | 15632 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C977 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#16840926 |
| commutator, socle | C2×C977 | C2×C4 |
| Fitting, prime radical | C22×C977 | C4 |
| cosocle | Dic977 | C22 |
| hypercenter | C22 | #16840926 |
| hypocenter | C977 | M16 |
| LCS | G ▷ C2×C977 ▷ C977 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7816 |
Polycyclic presentation:
2^4,977|a^2=c,c^2=d,b^a=bd,e^a=e^252,e^c=e^976986 conjugacy classes — view the full character table.
| maximal subgroup of | #44530726, #44530727, C2×#30627616, … |
| maximal normal subgroup of | #44530726, #44530727, C2×#30627616, … |
| maximal quotient of | #44530721, C22⋊#21463098, #44530733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15632, 49);