Finite Group DatabasebetaFinite Group Databasebeta| order | 31684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | C7921 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7921 | C4 |
| Frattini, socle | C89 | #67063 |
| prime radical, cosocle | D7921 | C2 |
| LCS | G ▷ C7921 | |
| UCS | C1 | |
9 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7921 |
Polycyclic presentation:
2^2,89^2|a^2=b,c^89=d^29,c^a=c^34d,d^a=d^34,c^b=c^88d^60,d^b=d^881984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31684, 4);