Finite Group DatabasebetaFinite Group Databasebeta| order | 31004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D337 |
| unambiguous semidirect product | (D23×C337)⋊C2 |
| unambiguous semidirect product | (C23×D337)⋊C2 |
| unambiguous semidirect product | D7751⋊C2 |
| Fitting, socle, derived, Hall | C23×C337 ⋊ C22 |
| Sylow | C337 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D337 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C337 | C22 |
| LCS | G ▷ C23×C337 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7751 |
2210 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31004, 8);