Finite Group DatabasebetaFinite Group Databasebeta| order | 2336 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C73 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#10596842 |
| commutator, socle | C2×C73 | C2×C8 |
| Fitting | C4×C73 | C8 |
| prime radical | C2×D73 | C8 |
| cosocle | #10596833 | C22 |
| hypercenter | C4 | #10596842 |
| hypocenter | C73 | M32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^5,73|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^10,f^b=f^72,f^c=f^27,f^d=f^7256 conjugacy classes — view the full character table.
| maximal subgroup of | #17989687, #17989688, #17989691, … |
| maximal normal subgroup of | #17989687, #17989688, #17989691, … |
| maximal quotient of | #17989681, #17989684, C4⋊#11924040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2336, 243);