Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C491 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D491 |
| commutator, socle | C2×C491 | C22×C4 |
| Fitting, prime radical | #41×C491 | C2 |
| cosocle | C4×C491 | C23 |
| hypercenter | #41 | D491 |
| hypocenter | C491 | #131 |
| LCS | G ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7856 |
Polycyclic presentation:
2^5,491|a^2=d,d^2=e,f^a=f^490,c^b=ce2470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44536839, #44536842, #44536844, … |
| maximal normal subgroup of | #44536839, #44536842, #44536844, … |
| maximal quotient of | #44536681, #44536692, #44536752, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 153);