Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×D29⋊C16 |
| unambiguous semidirect product | D29⋊(C2×C16) |
| derived, Sylow | C29 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1181 |
| commutator, hypocenter | C29 | C22×C16 |
| Frattini | C4 | C22×#1181 |
| Fitting | C2×C8×C29 | C4 |
| socle | C22×C29 | C2×C8 |
| prime radical | C22×D29 | C8 |
| cosocle | #6597 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C8 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#1181)⋊C16, #16834548, #16834549, … |
| maximal normal subgroup of | (C2×#1181)⋊C16, #16834548, #16834549, … |
| maximal quotient of | C4×D29⋊C16, C2×#14272049, D29⋊(C22⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1603);