Finite Group DatabasebetaFinite Group Databasebeta| order | 5612 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#6923 |
| Fitting, socle, Hall | C23×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #6923 |
| commutator, hypocenter | C61 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C61 | C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23 | |
12 conjugacy classes of subgroups.
437 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#6923⋊C3, C3×C23×#6923, C23×C3⋊#6923, … |
| maximal normal subgroup of | C23×#6923⋊C3, C3×C23×#6923, C23×#6923⋊C5, … |
| maximal quotient of | C3×C23×#6923, C23×C3⋊#6923, C5×C23×#6923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5612, 6);