Finite Group DatabasebetaFinite Group Databasebeta| order | 4356 |
| automorphism | Aut(G) order 1437480 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2178 |
| direct product | C2×D1089 |
| unambiguous semidirect product | (C2×C9)⋊D121 |
| unambiguous semidirect product | (C2×C121)⋊D9 |
| Fitting | C2×C9×C121 ⋊ C2 |
| derived, Hall | C9×C121 ⋊ C22 |
| Sylow | C121 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1089 |
| commutator, cosocle, hypocenter | C9×C121 | C22 |
| Frattini | C3×C11 | C2×D33 |
| Fitting | C2×C9×C121 | C2 |
| socle | C2×C3×C11 | D33 |
| LCS | G ▷ C9×C121 | |
| UCS | C1 ◁ C2 | |
45 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2178 |
1092 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9⋊(D121⋊C5), D5×D1089, C2×C5×D1089, … |
| maximal normal subgroup of | C2×C9⋊(D121⋊C5), C2×C5×D1089, C2×C7×D1089, … |
| maximal quotient of | D5×D1089, C2×C5×D1089, C2×D5445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4356, 10);