Finite Group DatabasebetaFinite Group Databasebeta| order | 12508 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×#6157 |
| Fitting, socle, Hall | C53×C59 ⋊ C4 |
| derived, Sylow | C53 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | #6157 |
| commutator, hypocenter | C53 | C4×C59 |
| Frattini | C1 | G |
| Fitting, socle | C53×C59 | C4 |
| prime radical | C59×D53 | C2 |
| cosocle | D53 | C2×C59 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C59 | |
12 conjugacy classes of subgroups.
1003 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C59×#6157, C59×C3⋊#6157 |
| maximal normal subgroup of | C3×C59×#6157 |
| maximal quotient of | C3×C59×#6157, C59×C3⋊#6157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12508, 6);