Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C491 ⋊ C2 |
| Sylow | C491 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D491 |
| commutator, socle, cosocle | C22×C491 | C23 |
| Fitting | C4⋊C4×C491 | C2 |
| prime radical | C2×D1964 | C2 |
| hypercenter | C4⋊C4 | D491 |
| hypocenter | C491 | #123 |
| LCS | G ▷ C22×C491 ▷ C491 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|c^2=d,b^a=bd,c^a=ce,f^a=f^490,f^b=f^4902464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D491, C2×#30628322, #44537234, … |
| maximal normal subgroup of | #123×D491, C2×#30628322, #44537234, … |
| maximal quotient of | #44536587, #44536596, #44536603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 131);