Finite Group DatabasebetaFinite Group Databasebeta| order | 2336 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C73 ⋊ C2 |
| Sylow | C73 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D73 |
| commutator, socle, cosocle | C22×C73 | C23 |
| Fitting | C2×Q8×C73 | C2 |
| prime radical | C2×D292 | C2 |
| hypercenter | C2×Q8 | D73 |
| hypocenter | C73 | #124 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^5,73|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^72,f^b=f^72,f^c=f^72374 conjugacy classes — view the full character table.
| maximal subgroup of | #17988383, #17988760, #17988762, … |
| maximal normal subgroup of | #17988383, #17988760, #17988762, … |
| maximal quotient of | #17988452, #17988477, #17988488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2336, 135);