Finite Group DatabasebetaFinite Group Databasebeta| order | 15784 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1973 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #21463563 |
| commutator, hypocenter | C1973 | C8 |
| Fitting, socle, prime radical | C2×C1973 | C4 |
| cosocle | Dic1973 | C2 |
| LCS | G ▷ C1973 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15784 |
Polycyclic presentation:
2^3,1973|a^2=b,b^2=c,d^a=d^259,d^b=d^1972994 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30628902, D1973⋊C8, #44538899, … |
| maximal normal subgroup of | C2×#30628902, D1973⋊C8, #44538899, … |
| maximal quotient of | #44538893, C2×#30628902 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15784, 13);