Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C73 ⋊ C2 |
| Sylow | C73 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D73 |
| commutator, socle, cosocle | C2×C73 | C23 |
| Frattini | C2 | C22×D73 |
| Fitting | C2×C4×C73 | C2 |
| hypercenter | C2×C4 | D73 |
| hypocenter | C73 | #41 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^4,73|c^2=d,b^a=bd,e^b=e^72298 conjugacy classes — view the full character table.
| maximal subgroup of | #14556517, #14556519, #14556597, … |
| maximal normal subgroup of | #14556517, #14556519, #14556597, … |
| maximal quotient of | #14556548, #14556550, C4×C22⋊D73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 40);