Finite Group DatabasebetaFinite Group Databasebeta| order | 15494 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C127 · Schur multiplier (H2) = C1 |
| direct product | D61×C127 |
| unambiguous semidirect product | C61⋊(C2×C127) |
| Fitting, socle, Hall | C61×C127 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C127 |
| Frattini | C1 | G |
| Fitting, socle | C61×C127 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C127 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7747 |
4064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C127×#6923, C127⋊#6923, D61×D127, … |
| maximal normal subgroup of | C127×#6923, C127⋊#6923, D61×D127, … |
| maximal quotient of | C127×Dic61, C2×D61×C127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15494, 1);