Finite Group DatabasebetaFinite Group Databasebeta| order | 31892 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D1139 |
| unambiguous semidirect product | (C2×C17)⋊(C7×D67) |
| unambiguous semidirect product | (C2×C67)⋊(C7×D17) |
| Fitting, socle | C2×C7×C17×C67 ⋊ C2 |
| derived, Hall | C17×C67 ⋊ C22×C7 |
| Hall | C7×C17×C67 ⋊ C22 |
| Hall | C7×C67 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×C7×D17 |
| Sylow | C17 ⋊ C2×C7×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D1139 |
| commutator, cosocle, hypocenter | C17×C67 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C17×C67 | C2 |
| LCS | G ▷ C17×C67 | |
| UCS | C1 ◁ C2×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15946 |
7994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31892, 23);