Finite Group DatabasebetaFinite Group Databasebeta| order | 24753 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C223 ⋊ C3 |
| Sylow | C223 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C223⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C223 | C3 |
| LCS | G ▷ C37×C223 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,37,223|b^a=b^26,c^a=c^392753 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#37613252, #60650095, #60650099, … |
| maximal normal subgroup of | C2×#37613252, #60650095, #60650099, … |
| maximal quotient of | C2×#37613252 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24753, 6);