Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| isoclinism | isoclinic class of D73 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D73 |
| Fitting | C2×C4×C73 ⋊ C2 |
| derived, Sylow | C73 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D73 |
| commutator, hypocenter | C73 | C22×C4 |
| Frattini | C2 | C22×D73 |
| Fitting | C2×C4×C73 | C2 |
| socle | C22×C73 | C22 |
| prime radical | C22×D73 | C2 |
| cosocle | C2×C73 | C23 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14556503, C42×D73, C22⋊C4×D73, … |
| maximal normal subgroup of | #14556503, C42×D73, C22⋊C4×D73, … |
| maximal quotient of | C42×D73, C2×C4×Dic73, C22⋊C4×D73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 32);