Finite Group DatabasebetaFinite Group Databasebeta| order | 11956 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×#6923 |
| Fitting, socle, Hall | C72×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | #6923 |
| commutator, hypocenter | C61 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C61 | C4 |
| prime radical | C72×D61 | C2 |
| cosocle | D61 | C2×C72 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C72 | |
60 conjugacy classes of subgroups.
931 conjugacy classes — view the full character table.
| maximal subgroup of | C72×#6923⋊C3, C7×#19103985, C7×#19103986, … |
| maximal normal subgroup of | C72×#6923⋊C3, C7×#19103985, C7×#19103986, … |
| maximal quotient of | C3×C72×#6923, C72×C3⋊#6923 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11956, 19);