Finite Group DatabasebetaFinite Group Databasebeta| order | 15794 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C149 · Schur multiplier (H2) = C1 |
| direct product | D53×C149 |
| unambiguous semidirect product | C53⋊(C2×C149) |
| Fitting, socle, Hall | C53×C149 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C149 | D53 |
| commutator, cosocle, hypocenter | C53 | C2×C149 |
| Frattini | C1 | G |
| Fitting, socle | C53×C149 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C149 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7897 |
4172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C149×#6157, #44539110, D53×D149, … |
| maximal normal subgroup of | C149×#6157, #44539110, D53×D149, … |
| maximal quotient of | C149×Dic53, C2×D53×C149 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15794, 1);