Finite Group DatabasebetaFinite Group Databasebeta| order | 1156 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic17 |
| derived | C17 ⋊ C4×C17 |
| Sylow | C172 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D17 |
| commutator, hypocenter | C17 | C4×C17 |
| Frattini | C2 | C17×D17 |
| Fitting, socle, prime radical | C2×C172 | C2 |
| cosocle | C2×C17 | C2×C17 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C17 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 68 |
340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16812392, C17×Dic51, C3×C17×Dic17, … |
| maximal normal subgroup of | C3×C17×Dic17, C11×C17×Dic17, C13×C17×Dic17, … |
| maximal quotient of | C17×Dic51, C3×C17×Dic17, C11×C17×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1156, 6);