Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#6599 |
| derived, Sylow | C29 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #1181 |
| commutator, hypocenter | C29 | C2×C4×C8 |
| Frattini | C22 | C22×#1181 |
| Fitting | C22×C4×C29 | C4 |
| socle, prime radical | C23×C29 | C2×C4 |
| cosocle | C2×Dic29 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C4 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16834314, #16834325, #16834328, … |
| maximal normal subgroup of | #16834314, #16834325, #16834328, … |
| maximal quotient of | C2×C8×#6599, C2×#14272004, M16×#6599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1504);