Finite Group DatabasebetaFinite Group Databasebeta| order | 25300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5⋊(C5⋊AGL(1,𝔽23)) |
| unambiguous semidirect product | (C2×C5)⋊(C5⋊AGL(1,𝔽23)) |
| unambiguous semidirect product | (C2×C23⋊C11)⋊(C5⋊D5) |
| unambiguous semidirect product | (C2×C5⋊D115)⋊C11 |
| Fitting, socle | C2×C52×C23 ⋊ C2×C11 |
| derived, Hall | C52×C23 ⋊ C22×C11 |
| Hall | C52×C23⋊C11 ⋊ C22 |
| Hall | C2×C5⋊D115 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×AGL(1,𝔽23) |
| Sylow | C23 ⋊ C2×C11×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(C5⋊AGL(1,𝔽23)) |
| commutator, cosocle, hypocenter | C52×C23 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C23 | C2×C11 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C2 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1150 |
358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25300, 91);