Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C73 ⋊ C2 |
| Sylow | C73 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D73 |
| commutator | C2×C73 | C2×C4 |
| Fitting | C2×C4×C73 | C2 |
| socle, cosocle | C22×C73 | C22 |
| prime radical | C22×D73 | C2 |
| hypercenter | C2×C4 | D73 |
| hypocenter | C73 | C22⋊C4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^4,73|a^2=d,b^a=bc,e^b=e^72298 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D73, C2×#11924005, #14556548, … |
| maximal normal subgroup of | C22⋊C4×D73, C2×#11924005, #14556548, … |
| maximal quotient of | #14556498, #14556503, #14556505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 17);