Finite Group DatabasebetaFinite Group Databasebeta| order | 32398 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C167 · Schur multiplier (H2) = C1 |
| direct product | C167×D97 |
| unambiguous semidirect product | C97⋊(C2×C167) |
| Fitting, socle, Hall | C97×C167 ⋊ C2 |
| derived, Sylow | C97 ⋊ C2×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | D97 |
| commutator, cosocle, hypocenter | C97 | C2×C167 |
| Frattini | C1 | G |
| Fitting, socle | C97×C167 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C167 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16199 |
8350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32398, 1);