Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C73 ⋊ C2 |
| Sylow | C73 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D292 |
| commutator, cosocle | C4×C73 | C22 |
| Frattini | C4 | C2×D73 |
| Fitting | C8×C73 | C2 |
| socle | C2×C73 | D4 |
| prime radical | D292 | C2 |
| hypercenter | C8 | D73 |
| hypocenter | C73 | SD16 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^4,73|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^72,c^b=cd,e^b=e^72295 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D73, C2×#11924017, #14556612, … |
| maximal normal subgroup of | SD16×D73, C2×#11924017, #14556612, … |
| maximal quotient of | #14556513, #14556516, #14556523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 29);