Finite Group DatabasebetaFinite Group Databasebeta| order | 15632 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C977 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16840926 |
| commutator, hypocenter | C977 | C2×C8 |
| Frattini | C2 | C2×#16840926 |
| Fitting | C4×C977 | C4 |
| socle | C2×C977 | C2×C4 |
| prime radical | C2×D977 | C4 |
| cosocle | Dic977 | C22 |
| LCS | G ▷ C977 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7816 |
Polycyclic presentation:
2^4,977|a^2=c,c^2=d,e^a=e^252,e^b=e^976,e^c=e^976992 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#16840926, #44530720, #44530728, … |
| maximal normal subgroup of | C8×#16840926, #44530720, #44530728, … |
| maximal quotient of | C4×#21463098, #44530723, #44530733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15632, 48);