Finite Group DatabasebetaFinite Group Databasebeta| order | 5820 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14515595⋊C3 |
| Fitting, socle, derived, Hall | C5×C97 ⋊ C3×C4 |
| Hall | #14515595 ⋊ C3 |
| Hall | C5×C97⋊C3 ⋊ C4 |
| Hall | C97⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C97 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #87604⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C97 | C3×C4 |
| LCS | G ▷ C5×C97 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,97|a^2=c,d^a=d^2,e^a=e^75,e^b=e^35,d^c=d^4,e^c=e^9655 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14515595⋊C3, C3⋊(#14515595⋊C3), #23753205⋊C3, … |
| maximal normal subgroup of | C3×#14515595⋊C3, C5×#14515595⋊C3 |
| maximal quotient of | #14515595⋊C9, C3×#14515595⋊C3, C3⋊(#14515595⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5820, 15);