Finite Group DatabasebetaFinite Group Databasebeta| order | 24892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic127⋊C49 |
| unambiguous semidirect product | (C127⋊C49)⋊C4 |
| derived, Sylow | C127 ⋊ C4×C49 |
| Hall | C127⋊C49 ⋊ C4 |
| Hall | Dic127 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C7 | D127⋊C7 |
| commutator, hypocenter | C127 | C4×C49 |
| Fitting, socle, prime radical, cosocle | C2×C7×C127 | C2×C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C7 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24892 |
Polycyclic presentation:
2,7,127,2,7|a^2=d,b^7=e,c^a=c^126,c^b=c^4322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24892, 2);