Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic73 |
| Sylow | C73 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D73 |
| commutator | C2×C73 | C2×C4 |
| Fitting, prime radical | C23×C73 | C2 |
| socle, cosocle | C22×C73 | C22 |
| hypercenter | C23 | D73 |
| hypocenter | C73 | C22⋊C4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^4,73|a^2=d,b^a=bc,e^a=e^72298 conjugacy classes — view the full character table.
| maximal subgroup of | #14556505, #14556506, C22⋊C4×D73, … |
| maximal normal subgroup of | #14556505, #14556506, C22⋊C4×D73, … |
| maximal quotient of | #14556498, C22⋊#10596831, #14556506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 18);