Finite Group DatabasebetaFinite Group Databasebeta| order | 8700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊#15668535 |
| Fitting, socle, derived, Hall | C3×C52×C29 ⋊ C4 |
| Hall | C52×C29 ⋊ Dic3 |
| Hall | C3×C29 ⋊ #1039 |
| Hall | C3×C52 ⋊ #1181 |
| Sylow | C29 ⋊ C3⋊#1039 |
| Sylow | C52 ⋊ C3⋊#1181 |
| Sylow | C3 ⋊ #15668535 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C29 | C4 |
| LCS | G ▷ C3×C52×C29 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,29|a^2=b,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^17,f^b=f^28603 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#15668535, C3⋊(#15668535⋊C3), C3×C3⋊#15668535, … |
| maximal normal subgroup of | C3⋊(#15668535⋊C3), C3×C3⋊#15668535 |
| maximal quotient of | C9⋊#15668535, C3×C3⋊#15668535, C3⋊(C3⋊#15668535) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8700, 122);