Finite Group DatabasebetaFinite Group Databasebeta| order | 15976 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1997 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #22547819 |
| commutator, hypocenter | C1997 | C8 |
| Fitting, socle, prime radical | C2×C1997 | C4 |
| cosocle | Dic1997 | C2 |
| LCS | G ▷ C1997 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15976 |
Polycyclic presentation:
2^3,1997|a^2=b,b^2=c,d^a=d^1585,d^b=d^19961006 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30630441, D1997⋊C8, #44544145, … |
| maximal normal subgroup of | C2×#30630441, D1997⋊C8, #44544145, … |
| maximal quotient of | #44544139, C2×#30630441 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15976, 13);