Finite Group DatabasebetaFinite Group Databasebeta| order | 31004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D337 |
| unambiguous semidirect product | C337⋊(C22×C23) |
| unambiguous semidirect product | (C2×C337)⋊(C2×C23) |
| Fitting, socle | C2×C23×C337 ⋊ C2 |
| derived, Sylow | C337 ⋊ C22×C23 |
| Hall | C23×C337 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D337 |
| commutator, cosocle, hypocenter | C337 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C337 | C2 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C2×C23 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15502 |
7820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31004, 9);