Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of #64423⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #64423⋊C4 |
| derived, Sylow | C72 ⋊ C2×C3×C4 |
| Hall | D7×Dic7 ⋊ C3 |
| Hall | #3861 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #64423⋊C2 |
| commutator, hypocenter | C72 | C2×C3×C4 |
| Fitting, socle, cosocle | C2×C72 | C22×C3 |
| prime radical | C2×#64423 | C2 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2^2,3,2,7^2|b^2=d,f^a=f^6,e^b=e^6,e^c=e^2,f^c=f^238 conjugacy classes — view the full character table.
| maximal subgroup of | #72214021, #72214035, #72214081, … |
| maximal normal subgroup of | #72214021, #72214035, #72214081, … |
| maximal quotient of | #72214774, #72219856, #72228718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 88);