Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25×C29 · Schur multiplier (H2) = C2 |
| Fitting, Hall | C22×C25×C29 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C25×C29 |
| Hall | C22×C29 ⋊ C3×C25 |
| Hall | C22×C25 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C29 | A4 |
| commutator, hypocenter | C22 | C3×C25×C29 |
| Frattini | C5 | C5×A4×C29 |
| Fitting | C22×C25×C29 | C3 |
| socle | C22×C5×C29 | C3×C5 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C25×C29 | |
30 conjugacy classes of subgroups.
2900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×A4×C25×C29 |
| maximal normal subgroup of | C3×A4×C25×C29 |
| maximal quotient of | C25×C29×C22⋊C9, C3×A4×C25×C29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 29);