Finite Group DatabasebetaFinite Group Databasebeta| order | 24753 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C223⋊C3)⋊C37 |
| unambiguous semidirect product | (C223⋊C37)⋊C3 |
| Fitting, socle, derived, Sylow | C223 ⋊ C3×C37 |
| Hall | C223⋊C37 ⋊ C3 |
| Hall | C223⋊C3 ⋊ C37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C223 | C3×C37 |
| LCS | G ▷ C223 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,37,223|c^a=c^183,c^b=c^60113 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C223⋊C3)⋊C37, AGL(1,𝔽223) |
| maximal normal subgroup of | C2×(C223⋊C3)⋊C37, AGL(1,𝔽223) |
| maximal quotient of | C2×(C223⋊C3)⋊C37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24753, 1);