Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of (#5997⋊C2)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (#5997⋊C2)⋊C3 |
| unambiguous semidirect product | (#5997⋊C3)⋊C2 |
| unambiguous semidirect product | (#64423⋊C2)⋊C2 |
| Fitting, socle, Sylow | C72 ⋊ C3×D4 |
| Hall | #5997⋊C2 ⋊ C3 |
| Hall | #3861 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C7⋊D7 | C22×C3 |
| Fitting, socle, hypocenter | C72 | C3×D4 |
| LCS | G ▷ C7⋊D7 ▷ C72 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 14 |
Polycyclic presentation:
2^2,3,2,7^2|b^a=bd,e^a=e^6,e^b=f^6,f^b=e^6,e^c=e^2,f^c=f^2,e^d=e^6,f^d=f^620 conjugacy classes — view the full character table.
| maximal subgroup of | #72224471, #72241578 |
| maximal normal subgroup of | #72224471 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 217);