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 ⋊ #67 |
| Sylow | C3 ⋊ #87641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×D21 |
| commutator, Fitting, socle, cosocle | C2×C3×C72 | C22 |
| hypocenter | C3×C72 | D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
Polycyclic presentation:
2^3,3,7^2|a^2=c,b^a=bc,d^a=d^2,e^a=e^6,f^b=f^6117 conjugacy classes — view the full character table.
| maximal subgroup of | #72222061, #72222096, D3×#87641, … |
| maximal normal subgroup of | #72222061, #72222096, D3×#87641, … |
| maximal quotient of | #72222167, C2×#11924249, #72269294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 164);