Finite Group DatabasebetaFinite Group Databasebeta| order | 31712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C991 ⋊ C2 |
| Sylow | C991 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D991 |
| commutator, cosocle | C4×C991 | C23 |
| Frattini | C4 | C22×D991 |
| Fitting | #41×C991 | C2 |
| socle | C2×C991 | C2×D4 |
| hypercenter | #41 | D991 |
| hypocenter | C991 | #135 |
| LCS | G ▷ C4×C991 ▷ C2×C991 ▷ C991 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15856 |
Polycyclic presentation:
2^5,991|c^2=e,d^2=e,b^a=bd,d^a=de,d^b=de,f^b=f^9904964 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31712, 166);