Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #64418⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #64418⋊C4 |
| derived, Hall | #3862 ⋊ C2×C4 |
| Sylow | C72 ⋊ C4×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #64418⋊C2 |
| commutator, hypocenter | #3862 | C2×C4 |
| Fitting, socle | C2×C72 | C2×D3 |
| prime radical | C2×#64418 | C2 |
| cosocle | C2×#3862 | C22 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2^3,3,7^2|a^2=c,e^a=e^6,f^a=f^6,d^b=d^2,e^b=f^3,f^b=e^5,e^d=e^4,f^d=f^238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 77);