Finite Group DatabasebetaFinite Group Databasebeta| order | 1150 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D23 |
| unambiguous semidirect product | C23⋊(C2×C25) |
| Fitting, Hall | C23×C25 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D23 |
| commutator, hypocenter | C23 | C2×C25 |
| Frattini | C5 | C5×D23 |
| Fitting | C23×C25 | C2 |
| socle, cosocle | C5×C23 | C2×C5 |
| prime radical | C5×D23 | C5 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 575 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D25, C2×C25×D23, C3×C25×D23, … |
| maximal normal subgroup of | D23×D25, C2×C25×D23, C3×C25×D23, … |
| maximal quotient of | C25×Dic23, C2×C25×D23, C3×C25×D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1150, 2);