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 | C4×D29⋊C8 |
| derived, Sylow | C29 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #1181 |
| commutator, hypocenter | C29 | C2×C4×C8 |
| Frattini | C22 | C22×#1181 |
| Fitting | C42×C29 | C4 |
| socle | C22×C29 | C22×C4 |
| prime radical | C22×D29 | C2×C4 |
| cosocle | C2×Dic29 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C42 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16834321, #16834323, #16834326, … |
| maximal normal subgroup of | #16834321, #16834323, #16834326, … |
| maximal quotient of | C8×D29⋊C8, #16834686, #16834690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1505);