Finite Group DatabasebetaFinite Group Databasebeta| order | 31684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C89 |
No aliases for this group.
| derived, Sylow | C892 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C89⋊D89 |
| commutator, hypocenter | C892 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C892 | C2 |
| LCS | G ▷ C892 | |
| UCS | C1 ◁ C2 | |
276 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31684 |
Polycyclic presentation:
2,89^2,2|a^2=d,b^a=b^88,c^a=c^887924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31684, 8);