Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#6599 |
| derived, Sylow | C29 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1181 |
| commutator, hypocenter | C29 | C82 |
| Frattini | C2×C4 | C2×#1181 |
| Fitting | C2×C8×C29 | C4 |
| socle, prime radical | C22×C29 | C42 |
| cosocle | C4×Dic29 | C22 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#6599, #16834403, #6599⋊C16, … |
| maximal normal subgroup of | C16×#6599, #16834403, #6599⋊C16, … |
| maximal quotient of | #16834314, C16×#6599, C8×#90770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1389);