Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#64470 |
| derived, Hall | C52⋊C3 ⋊ C4×C29 |
| Hall | C29×C52⋊C3 ⋊ C4 |
| Hall | C52×C29 ⋊ Dic3 |
| Sylow | C52 ⋊ Dic3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C29 | #3874 |
| commutator, hypocenter | C52⋊C3 | C4×C29 |
| Frattini | C2 | C29×#3874 |
| Fitting, socle | C2×C52×C29 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C2×C29 | |
36 conjugacy classes of subgroups.
754 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C29×#64470, C29×C3⋊#64470 |
| maximal normal subgroup of | C3×C29×#64470 |
| maximal quotient of | C29×#11744607, C3×C29×#64470, C29×C3⋊#64470 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 38);