Finite Group DatabasebetaFinite Group Databasebeta| order | 10603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C461⋊C23 |
| Fitting, socle, derived, Sylow | C461 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C461 | C23 |
| LCS | G ▷ C461 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
23,461|b^a=b^26243 conjugacy classes — view the full character table.
| maximal subgroup of | D461⋊C23, C2×C461⋊C23, C3×C461⋊C23 |
| maximal normal subgroup of | D461⋊C23, C2×C461⋊C23, C3×C461⋊C23 |
| maximal quotient of | C2×C461⋊C23, C3×C461⋊C23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10603, 1);