Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×#6599 |
| derived, Sylow | C29 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #1181 |
| commutator, hypocenter | C29 | C23×C8 |
| Frattini | C2 | C23×#1181 |
| Fitting, socle, prime radical | C24×C29 | C4 |
| cosocle | Dic29 | C24 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C24 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14272029, #16835158, C22⋊C4×#6599, … |
| maximal normal subgroup of | C2×#14272029, #16835158, C22⋊C4×#6599, … |
| maximal quotient of | C22×C4×#6599, C22×C22⋊#6599, C22×C4⋊#6599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1619);