Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| isoclinism | isoclinic class of #10596842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#10596842 |
| Fitting, socle | C2×C73 ⋊ C8 |
| derived, Sylow | C73 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10596842 |
| commutator, hypocenter | C73 | C2×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C73 | C8 |
| prime radical | C2×D73 | C4 |
| cosocle | #64408 | C22 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 146 |
34 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10596842, C22⋊#10596842, C4⋊#10596842, … |
| maximal normal subgroup of | C4×#10596842, C22⋊#10596842, C4⋊#10596842, … |
| maximal quotient of | C4×#10596842, C22⋊#10596842, C4⋊#10596842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 53);