Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×(C23⋊C11)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C23⋊C11)⋊(C5×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C23⋊AGL(1,𝔽5))⋊(C5×C11) |
| unambiguous semidirect product | (C5×C23⋊AGL(1,𝔽5))⋊C11 |
| Fitting, socle, Hall | C52×C23 ⋊ C4×C11 |
| derived | C5×C23 ⋊ C4×C5×C11 |
| Hall | C52×C23⋊C11 ⋊ C4 |
| Hall | C5×C23⋊AGL(1,𝔽5) ⋊ C11 |
| Hall | C23⋊C11 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ Dic23⋊C11 |
| Sylow | C23 ⋊ C5×C11×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C23⋊C11)⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C23 | C4×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C23 | C4×C11 |
| prime radical | C5×D5×C23⋊C11 | C2 |
| cosocle | D5×C23 | C2×C5×C11 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 460 |
295 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 76);