Finite Group DatabasebetaFinite Group Databasebeta| order | 12580 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C17×C37 ⋊ C4 |
| Hall | C17×C37 ⋊ AGL(1,𝔽5) |
| Hall | C5×C37 ⋊ #595 |
| Hall | C5×C17 ⋊ #3866 |
| Sylow | C37 ⋊ #66776 |
| Sylow | C17 ⋊ #10625191 |
| Sylow | C5 ⋊ #14578980 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C17×C37 | C4 |
| prime radical, cosocle | D3145 | C2 |
| LCS | G ▷ C5×C17×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,17,37|a^2=b,c^a=c^2,d^a=d^4,e^a=e^31,c^b=c^4,d^b=d^16,e^b=e^36790 conjugacy classes — view the full character table.
| maximal subgroup of | #27160374⋊C3, C3×#27160374, C3⋊#27160374 |
| maximal normal subgroup of | #27160374⋊C3, C3×#27160374 |
| maximal quotient of | C3×#27160374, C3⋊#27160374 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12580, 26);