Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C491 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D491 |
| commutator, socle, prime radical, cosocle | C22×C491 | C23 |
| Fitting | C2×Q8×C491 | C2 |
| hypercenter | C2×Q8 | D491 |
| hypocenter | C491 | C4⋊Q8 |
| LCS | G ▷ C22×C491 ▷ C491 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
Polycyclic presentation:
2^5,491|a^2=d,b^2=d,c^2=e,b^a=bd,c^a=ce,f^c=f^4902464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536523, #44536906, #44536908, … |
| maximal normal subgroup of | #44536523, #44536906, #44536908, … |
| maximal quotient of | #44536594, #44536620, #44536630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 144);