Finite Group DatabasebetaFinite Group Databasebeta| order | 31004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#13062438 |
| Fitting, socle, Hall | C23×C337 ⋊ C4 |
| derived, Sylow | C337 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #13062438 |
| commutator, hypocenter | C337 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C337 | C4 |
| prime radical | C23×D337 | C2 |
| cosocle | D337 | C2×C23 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C23 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7751 |
2024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31004, 6);