Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | ΓL(1,𝔽8)×C22⋊D7 |
| Fitting | C22×C72 ⋊ C2×C3 |
| Hall | C7×C22⋊D7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ D4 |
| Sylow | C72 ⋊ C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D7×ΓL(1,𝔽8) |
| commutator, socle, cosocle | C2×C72 | C22×C3 |
| Fitting | C22×C72 | C2×C3 |
| hypercenter | C22 | D7×ΓL(1,𝔽8) |
| hypocenter | C72 | C3×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ C22 | |
69 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 112);