Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D49⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D49⋊A4 |
| unambiguous semidirect product | (C22⋊(C49⋊C3))⋊C2 |
| Fitting, derived | C22×C49 ⋊ C2×C3 |
| Hall | C22×D49 ⋊ C3 |
| Sylow | C49 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C22×C49 | C2×C3 |
| Frattini | C7 | D7⋊A4 |
| socle | C22×C7 | AGL(1,𝔽7) |
| LCS | G ▷ C22×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 196 |
Polycyclic presentation:
2,3,2^2,7^2|e^7=f,e^a=e^6f^6,f^a=f^6,c^b=cd,d^b=c,e^b=e^4f^2,f^b=f^440 conjugacy classes — view the full character table.
| maximal subgroup of | A4×D49⋊C3, #72275483 |
| maximal normal subgroup of | A4×D49⋊C3, #72275483 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 48);