Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×D29⋊C8 |
| unambiguous semidirect product | D29⋊(C22×C8) |
| derived, Sylow | C29 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #1181 |
| commutator, hypocenter | C29 | C23×C8 |
| Frattini | C2 | C23×#1181 |
| Fitting | C22×C4×C29 | C4 |
| socle | C23×C29 | C2×C4 |
| prime radical | C23×D29 | C4 |
| cosocle | Dic29 | C24 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C4 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C2×#1181)⋊C8, #16835153, #16835159, … |
| maximal normal subgroup of | C2×(C2×#1181)⋊C8, #16835153, #16835159, … |
| maximal quotient of | C22×C4×#6599, C2×C4×D29⋊C8, C2×D29⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1620);