Finite Group DatabasebetaFinite Group Databasebeta| order | 1192 |
| isoclinism | isoclinic class of #10597010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#10597010 |
| unambiguous semidirect product | D149⋊C4 |
| Fitting, socle | C2×C149 ⋊ C4 |
| derived, Sylow | C149 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10597010 |
| commutator, hypocenter | C149 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C149 | C4 |
| prime radical | C2×D149 | C2 |
| cosocle | D149 | C22 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 298 |
82 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10597010, C22⋊#10597010, C4⋊#10597010, … |
| maximal normal subgroup of | C4×#10597010, C22⋊#10597010, C4⋊#10597010, … |
| maximal quotient of | C4×#10597010, C22⋊#10597010, C4⋊#10597010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1192, 14);