Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #10596885⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10596885⋊C2 |
| unambiguous semidirect product | (#64418⋊C2)⋊C2 |
| unambiguous semidirect product | (#64422⋊C2)⋊C2 |
| Fitting, socle, Sylow | C72 ⋊ #67 |
| Hall | #3862 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | #64425 | C22 |
| Fitting, socle | C72 | #67 |
| hypocenter | #3862 | D4 |
| LCS | G ▷ #64425 ▷ #3862 | |
| UCS | C1 | |
47 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 14 |
Polycyclic presentation:
2^3,3,7^2|b^a=bc,e^a=e^6,d^b=d^2,e^b=f^4,f^b=e^2,e^c=e^6,f^c=f^6,e^d=e^4,f^d=f^217 conjugacy classes — view the full character table.
| maximal subgroup of | #72241578 |
| maximal normal subgroup of | #72241578 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 216);