Finite Group DatabasebetaFinite Group Databasebeta| order | 10120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×AGL(1,𝔽23) |
| Fitting, socle | C2×C5×C23 ⋊ C22×C11 |
| derived, Hall | C5×C23 ⋊ C23×C11 |
| Hall | C5×C23⋊C11 ⋊ C23 |
| Hall | C2×D5×D23 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C22×D5 |
| Sylow | C23 ⋊ C22×D5×C11 |
| Sylow | C5 ⋊ C22×AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C5×C23 | C23×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C23 | C22×C11 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 230 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×AGL(1,𝔽23) |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×AGL(1,𝔽23) |
Past the SmallGroups library coverage — no SmallGroups id.