Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C491 ⋊ C2 |
| Sylow | C491 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D491 |
| commutator, cosocle | C4×C491 | C23 |
| Frattini | C4 | C22×D491 |
| Fitting | #41×C491 | C2 |
| socle | C2×C491 | C2×D4 |
| hypercenter | #41 | D491 |
| hypocenter | C491 | #135 |
| LCS | G ▷ C4×C491 ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
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,d^b=de,f^b=f^4902464 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536839, #44536840, #44536844, … |
| maximal normal subgroup of | #44536839, #44536840, #44536844, … |
| maximal quotient of | #44536719, #44536721, #44536761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 166);