Finite Group DatabasebetaFinite Group Databasebeta| order | 23700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×(C79⋊C3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C79⋊C3)⋊(C5×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C79⋊AGL(1,𝔽5))⋊(C3×C5) |
| unambiguous semidirect product | (C5×C79⋊AGL(1,𝔽5))⋊C3 |
| Fitting, socle, Hall | C52×C79 ⋊ C3×C4 |
| derived | C5×C79 ⋊ C3×C4×C5 |
| Hall | C5×C79⋊AGL(1,𝔽5) ⋊ C3 |
| Hall | C52×C79⋊C3 ⋊ C4 |
| Hall | C79⋊C3 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C79 ⋊ C3×C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ (C79⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C79⋊C3)⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C79 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C79 | C3×C4 |
| prime radical | C5×D5×C79⋊C3 | C2 |
| cosocle | D5×C79 | C2×C3×C5 |
| LCS | G ▷ C5×C79 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1580 |
335 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23700, 83);