Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C491 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D491 |
| commutator | C2×C491 | C22×C4 |
| Fitting | C4⋊C4×C491 | C2 |
| socle, prime radical, cosocle | C22×C491 | C23 |
| hypercenter | C4⋊C4 | D491 |
| hypocenter | C491 | C4×Q8 |
| LCS | G ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15712 |
Polycyclic presentation:
2^5,491|a^2=e,b^2=d,c^2=de,b^a=bd,f^c=f^4902470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536812, #44536816, #44536817, … |
| maximal normal subgroup of | #44536812, #44536816, #44536817, … |
| maximal quotient of | #44536576, C4⋊C4×Dic491, #44536606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 111);