Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#64423 |
| Fitting | C4×C72 ⋊ C2×C3 |
| Hall | C7×D28 ⋊ C3 |
| Hall | #3861 ⋊ D4 |
| Sylow | C72 ⋊ C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#64423 |
| commutator, socle, cosocle | C2×C72 | C22×C3 |
| Fitting | C4×C72 | C2×C3 |
| hypercenter | C4 | #64423 |
| hypocenter | C72 | C3×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ C4 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2^2,3,2,7^2|b^2=d,b^a=bd,e^a=e^6,e^c=e^4,f^c=f^453 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#64423, #72214041, #72214061, … |
| maximal normal subgroup of | D4×#64423, #72214041, #72214061, … |
| maximal quotient of | #72214763, #72228618, #72228625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 120);