Finite Group DatabasebetaFinite Group Databasebeta| order | 11834 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×D61 |
| unambiguous semidirect product | C61⋊(C2×C97) |
| Fitting, socle, Hall | C61×C97 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C97 |
| Frattini | C1 | G |
| Fitting, socle | C61×C97 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C97 | |
8 conjugacy classes of subgroups.
3104 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C97×#6923, #37556933, D61×D97, … |
| maximal normal subgroup of | C97×#6923, #37556933, D61×D97, … |
| maximal quotient of | C97×Dic61, C2×C97×D61, C3×C97×D61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11834, 1);