Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of #90646 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#90646 |
| derived, Hall | C52⋊C9 ⋊ C2×C23 |
| Hall | C23×C52⋊C9 ⋊ C2 |
| Hall | C52×C23 ⋊ D9 |
| Sylow | C52 ⋊ D9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #90646 |
| commutator, cosocle, hypocenter | C52⋊C9 | C2×C23 |
| Frattini | C3 | C23×#3874 |
| Fitting, socle | C3×C52×C23 | D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C23 | |
40 conjugacy classes of subgroups.
552 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#90646⋊C2, #90646⋊D23, D23×#90646, … |
| maximal normal subgroup of | C23×#90646⋊C2, #90646⋊D23, D23×#90646, … |
| maximal quotient of | C23×#11744607, C2×C23×#90646 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 22);