Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C29 ⋊ C2 |
| Sylow | C29 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D29 |
| commutator, socle | C2×C29 | C23×C4 |
| Fitting | C2×M16×C29 | C2 |
| prime radical | C2×#90805 | C2 |
| cosocle | C4×C29 | C24 |
| hypercenter | C2×M16 | D29 |
| hypocenter | C29 | #568 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=e,e^2=f,d^a=df,c^b=cf,g^c=g^28314 conjugacy classes — view the full character table.
| maximal subgroup of | #16819710, #16819713, #16819729, … |
| maximal normal subgroup of | #16819710, #16819713, #16819729, … |
| maximal quotient of | #16827909, #16827910, #16827917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1315);