Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C491 ⋊ C2 |
| Sylow | C491 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D491 |
| commutator, cosocle | C4×C491 | C23 |
| Frattini | C4 | C22×D491 |
| Fitting | Q16×C491 | C2 |
| socle | C2×C491 | C2×D4 |
| hypercenter | Q16 | D491 |
| hypocenter | C491 | #135 |
| LCS | G ▷ C4×C491 ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^490,d^b=de,f^b=f^490,f^c=f^4901729 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44537156, #44537158, #44537162, … |
| maximal normal subgroup of | #44537156, #44537158, #44537162, … |
| maximal quotient of | #44536720, #44536762, #44536807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 169);