Finite Group DatabasebetaFinite Group Databasebeta| order | 9836 |
| automorphism | Aut(G) order 12088444 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4918 |
| direct product | C2×D2459 |
| unambiguous semidirect product | C2459⋊C22 |
| unambiguous semidirect product | (C2×C2459)⋊C2 |
| Fitting, socle | C2×C2459 ⋊ C2 |
| derived, Sylow | C2459 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2459 |
| commutator, cosocle, hypocenter | C2459 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C2459 | C2 |
| LCS | G ▷ C2459 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
2462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D2459, C22⋊D2459, D9836, … |
| maximal normal subgroup of | C4×D2459, C22⋊D2459, D9836, … |
| maximal quotient of | C4×D2459, C2×Dic2459, C22⋊D2459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9836, 3);