Finite Group DatabasebetaFinite Group Databasebeta| order | 31712 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C991 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D991 |
| commutator | C2×C991 | C22×C4 |
| Fitting | C4⋊C4×C991 | C2 |
| socle, prime radical, cosocle | C22×C991 | C23 |
| hypercenter | C4⋊C4 | D991 |
| hypocenter | C991 | C4×Q8 |
| LCS | G ▷ C2×C991 ▷ C991 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31712 |
Polycyclic presentation:
2^5,991|a^2=e,b^2=d,c^2=de,b^a=bd,f^c=f^9904970 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31712, 111);