Finite Group DatabasebetaFinite Group Databasebeta| order | 24549 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C167 · Schur multiplier (H2) = C1 |
| direct product | C49⋊C3×C167 |
| unambiguous semidirect product | C49⋊(C3×C167) |
| unambiguous semidirect product | (C49×C167)⋊C3 |
| Fitting, Hall | C49×C167 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C3×C167 |
| Frattini | C7 | ΓL(1,𝔽8)×C167 |
| Fitting | C49×C167 | C3 |
| socle | C7×C167 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C167 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8183 |
3173 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24549, 2);