Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#90646 |
| derived, Hall | C23×C52⋊C9 ⋊ C2 |
| Hall | C52×C23 ⋊ D9 |
| Hall | C52⋊C9 ⋊ D23 |
| Sylow | C52 ⋊ D207 |
| Sylow | C23 ⋊ #90646 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C23×C52⋊C9 | C2 |
| Frattini | C3 | C23⋊#3874 |
| Fitting, socle | C3×C52×C23 | D3 |
| LCS | G ▷ C23×C52⋊C9 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,5^2,3|b^3=f^2,b^a=b^2f,c^a=c^22,d^a=d^2e,e^a=d^2e^3,f^a=f^2,d^b=d^2e^4,e^b=d^2e^2387 conjugacy classes — view the full character table.
| maximal subgroup of | #90646⋊D23, ((C5⋊D5)⋊C9)⋊D23, D23×#90646, … |
| maximal normal subgroup of | #90646⋊D23, ((C5⋊D5)⋊C9)⋊D23, D23×#90646, … |
| maximal quotient of | C23⋊#11744607, C2×C23⋊#90646 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 23);