Finite Group DatabasebetaFinite Group Databasebeta| order | 31972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C7993 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7993 | C4 |
| prime radical, cosocle | D7993 | C2 |
| LCS | G ▷ C7993 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7993 |
Polycyclic presentation:
2^2,7993|a^2=b,c^a=c^2110,c^b=c^79922002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31972, 3);