Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C72 ⋊ D4 |
| Sylow | C72 ⋊ D12 |
| Sylow | C3 ⋊ #87640 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D21⋊D7 |
| commutator, Fitting, socle, cosocle | C2×C3×C72 | C22 |
| hypocenter | C3×C72 | D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^3,3,7^2|b^2=c,b^a=bc,d^a=d^2,e^a=e^6,e^b=e^6,f^b=f^699 conjugacy classes — view the full character table.
| maximal subgroup of | #72246460, D3×#87640, #72246472, … |
| maximal normal subgroup of | #72246460, D3×#87640, #72246472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 169);