Finite Group DatabasebetaFinite Group Databasebeta| order | 1192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D149 |
| Fitting | C22×C149 ⋊ C2 |
| Sylow | C149 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D149 |
| commutator, socle, cosocle | C2×C149 | C22 |
| Fitting | C22×C149 | C2 |
| hypercenter | C22 | D149 |
| hypocenter | C149 | D4 |
| LCS | G ▷ C2×C149 ▷ C149 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 153 |
| transitive degree | μt(G) = 596 |
Polycyclic presentation:
2^3,149|b^a=bc,d^b=d^148301 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D149, C2×C22⋊D149, #14558735, … |
| maximal normal subgroup of | D4×D149, C2×C22⋊D149, #14558735, … |
| maximal quotient of | #14558713, C22⋊Dic149, #14558715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1192, 9);