Finite Group DatabasebetaFinite Group Databasebeta| order | 31712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C991 ⋊ C2 |
| Sylow | C991 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D991 |
| commutator, socle, cosocle | C22×C991 | C23 |
| Fitting | C24×C991 | C2 |
| hypercenter | C24 | D991 |
| hypocenter | C991 | #120 |
| LCS | G ▷ C22×C991 ▷ C991 | |
| UCS | C1 ◁ C22 ◁ C24 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7928 |
Polycyclic presentation:
2^5,991|b^a=bd,c^a=ce,f^a=f^9907934 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31712, 115);