Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C29×C52⋊C3 ⋊ C4 |
| Hall | C52×C29 ⋊ Dic3 |
| Hall | C52⋊C3 ⋊ Dic29 |
| Sylow | C29 ⋊ #64470 |
| Sylow | C52 ⋊ Dic87 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C29⋊#3874 |
| commutator, hypocenter | C29×C52⋊C3 | C4 |
| Fitting, socle | C2×C52×C29 | D3 |
| LCS | G ▷ C29×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,5^2,2|a^2=f,b^a=b^2,c^a=c^28,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^2334 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#22576397, C3⋊#22576397 |
| maximal normal subgroup of | C3×#22576397 |
| maximal quotient of | #39907817, C3×#22576397, C3⋊#22576397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 39);