Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D7×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| Fitting, socle | C2×C72 ⋊ C22×C3 |
| derived, Sylow | C72 ⋊ C23×C3 |
| Hall | C2×D72 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C72 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2 | |
133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽7)2, #72222021, D3×D7×AGL(1,𝔽7), … |
| maximal normal subgroup of | C2×AGL(1,𝔽7)2, #72222021, #72245001, … |
| maximal quotient of | #72222021, D3×D7×AGL(1,𝔽7), C2×(ΓL(1,𝔽8)⋊D7)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 228);