Finite Group DatabasebetaFinite Group Databasebeta| order | 11825 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×C11⋊C25 |
| unambiguous semidirect product | C11⋊(C25×C43) |
| unambiguous semidirect product | (C11×C43)⋊C25 |
| derived, Sylow | C11 ⋊ C25×C43 |
| Hall | C11×C43 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C43 | C11⋊C5 |
| commutator, hypocenter | C11 | C25×C43 |
| Frattini | C5 | C43×C11⋊C5 |
| Fitting, socle, prime radical | C5×C11×C43 | C5 |
| cosocle | C5×C11 | C5×C43 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C43 | |
12 conjugacy classes of subgroups.
1505 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C43×C11⋊C25, D43×C11⋊C25, C43×D11⋊C25, … |
| maximal normal subgroup of | C2×C43×C11⋊C25, D43×C11⋊C25, C43×D11⋊C25, … |
| maximal quotient of | C2×C43×C11⋊C25, C3×C43×C11⋊C25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11825, 2);