Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C25×#1181 |
| Fitting, Hall | C3×C25×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C3×C4×C25 |
| Hall | C25×C29 ⋊ C3×C4 |
| Hall | C3×C29 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | #1181 |
| commutator, hypocenter | C29 | C3×C4×C25 |
| Frattini | C5 | C3×C5×#1181 |
| Fitting | C3×C25×C29 | C4 |
| socle | C3×C5×C29 | C4×C5 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C3×C25 | |
36 conjugacy classes of subgroups.
825 conjugacy classes — view the full character table.
| maximal subgroup of | C9×C25×#1181, C32×C25×#1181, C3×C25×C3⋊#1181 |
| maximal normal subgroup of | C9×C25×#1181, C32×C25×#1181 |
| maximal quotient of | C9×C25×#1181, C32×C25×#1181, C3×C25×C3⋊#1181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 10);