Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of A4×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×A4×D7 |
| Fitting, socle | C22×C72 ⋊ C2×C3 |
| derived | C22×C7 ⋊ C2×C3×C7 |
| Hall | C22×C7×D7 ⋊ C3 |
| Sylow | C72 ⋊ C2×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | A4×D7 |
| commutator, cosocle, hypocenter | C22×C7 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72 | C2×C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C7 | |
63 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#10620796, A4×#64423, A4×D72, … |
| maximal normal subgroup of | A4×#64423, A4×D72, C7×D7×S4, … |
| maximal quotient of | C7×#10620796, A4×D49⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 252);