Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C29 ⋊ C4 |
| Sylow | C29 ⋊ #520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#1181 |
| commutator, socle | C2×C29 | C23×C4 |
| Fitting | #41×C29 | C4 |
| prime radical | #41×D29 | C2 |
| cosocle | C2×D29 | C24 |
| hypercenter | #41 | #1181 |
| hypocenter | C29 | #520 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ #41 | |
294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^6,29|a^2=f,d^2=e,b^a=be,d^a=de,g^a=g^12,c^b=ce,g^f=g^28104 conjugacy classes — view the full character table.
| maximal subgroup of | #16835451, #16835452, #16835491, … |
| maximal normal subgroup of | #16835451, #16835452, #16835491, … |
| maximal quotient of | #16835929, #16835931, #16835932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1618);