Finite Group DatabasebetaFinite Group Databasebeta| order | 11956 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C61 · Schur multiplier (H2) = C2 |
| direct product | D72×C61 |
| unambiguous semidirect product | (C7×D7)⋊(C2×C61) |
| unambiguous semidirect product | (C7⋊D7)⋊(C2×C61) |
| Fitting, socle, Hall | C72×C61 ⋊ C22 |
| derived, Sylow | C72 ⋊ C22×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D72 |
| commutator, cosocle, hypocenter | C72 | C22×C61 |
| Frattini | C1 | G |
| Fitting, socle | C72×C61 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C61 | |
52 conjugacy classes of subgroups.
1525 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C61×#64418⋊C2, D7×AGL(1,𝔽7)×C61, D7×#14579425, … |
| maximal normal subgroup of | D7×AGL(1,𝔽7)×C61, D7×#14579425, D7×#14579424, … |
| maximal quotient of | C3×D72×C61, D7×D21×C61, C61×D21⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11956, 24);