Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C73 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#64408 |
| commutator, socle | C2×C73 | C2×C4 |
| Fitting, prime radical | C22×C73 | C4 |
| cosocle | Dic73 | C22 |
| hypercenter | C22 | #64408 |
| hypocenter | C73 | M16 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^4,73|a^2=c,c^2=d,b^a=bd,e^a=e^27,e^c=e^7282 conjugacy classes — view the full character table.
| maximal subgroup of | #14556651, #14556652, C2×#11924037, … |
| maximal normal subgroup of | #14556651, #14556652, C2×#11924037, … |
| maximal quotient of | #14556646, C22⋊#10596833, #14556658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 49);