Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C491 ⋊ C2 |
| Sylow | C491 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D491 |
| commutator, socle | C2×C491 | C2×C8 |
| Fitting | C16×C491 | C2 |
| prime radical | C2×D491 | C8 |
| cosocle | C8×C491 | C22 |
| hypercenter | C16 | D491 |
| hypocenter | C491 | M32 |
| LCS | G ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=c,c^2=d,d^2=e,b^a=be,f^b=f^4903940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M32×D491, C2×#30628276, #44537141, … |
| maximal normal subgroup of | M32×D491, C2×#30628276, #44537141, … |
| maximal quotient of | #44536500, (C2×D491)⋊C16, Dic491⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 85);