Finite Group DatabasebetaFinite Group Databasebeta| order | 11956 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C7 |
| direct product | C61×#5997 |
| Fitting, socle, Hall | C72×C61 ⋊ C4 |
| derived, Sylow | C72 ⋊ C4×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | #5997 |
| commutator, hypocenter | C72 | C4×C61 |
| Frattini | C1 | G |
| Fitting, socle | C72×C61 | C4 |
| prime radical | C61×C7⋊D7 | C2 |
| cosocle | C7⋊D7 | C2×C61 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C61 | |
28 conjugacy classes of subgroups.
976 conjugacy classes — view the full character table.
| maximal subgroup of | C61⋊C3×#5997, C61×#10596885, C61×#5997⋊C3, … |
| maximal normal subgroup of | C61⋊C3×#5997, C61×#5997⋊C3, #49089816, … |
| maximal quotient of | C3×C61×#5997, C61×C3⋊#5997 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11956, 27);