Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #11924318 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C3×C72 ⋊ D4 |
| Sylow | C72 ⋊ #67 |
| Sylow | C3 ⋊ #5997⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C3×C7⋊D7 | C22 |
| Fitting, socle, hypocenter | C3×C72 | D4 |
| LCS | G ▷ C3×C7⋊D7 ▷ C3×C72 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 42 |
Polycyclic presentation:
2^3,3,7^2|b^a=bc,d^a=d^2,e^a=f,f^a=e,e^b=e^6,e^c=e^6,f^c=f^645 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 233);