Finite Group DatabasebetaFinite Group Databasebeta| order | 15728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C983 ⋊ C2 |
| Sylow | C983 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D983 |
| commutator, socle, cosocle | C2×C983 | C23 |
| Fitting | Q8×C983 | C2 |
| hypercenter | Q8 | D983 |
| hypocenter | C983 | #41 |
| LCS | G ▷ C2×C983 ▷ C983 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7864 |
Polycyclic presentation:
2^4,983|c^2=d,b^a=bd,e^a=e^982,e^b=e^982,e^c=e^9822465 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44537984, #44537986, #44537990, … |
| maximal normal subgroup of | #44537984, #44537986, #44537990, … |
| maximal quotient of | #44537921, #44537925, Q8×Dic983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15728, 41);