Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C29 ⋊ #391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D29 |
| commutator | C22×C29 | C22×C4 |
| Fitting | C29×#95 | C2 |
| socle, prime radical, cosocle | C23×C29 | C23 |
| hypercenter | #95 | D29 |
| hypocenter | C29 | #391 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #95 | |
186 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^c=g^28308 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#391, C2×#14271067, #16821964, … |
| maximal normal subgroup of | D29×#391, C2×#14271067, #16821964, … |
| maximal quotient of | #16817720, #16817723, #16817726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 453);