Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C7 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×C7×D7 |
| Fitting, socle | C22×C3×C72 ⋊ C2 |
| derived | C7 ⋊ C23×C3×C7 |
| Hall | C3×C72 ⋊ C23 |
| Sylow | C72 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C7 | D7 |
| commutator, cosocle, hypocenter | C7 | C23×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C72 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C22×C3×C7 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3×D72, C22×D3×C7×D7, C22×D7×D21, … |
| maximal normal subgroup of | C22×C3×D72, C22×D3×C7×D7, C22×D7×D21, … |
| maximal quotient of | C2×C3×C7×C22⋊D7, C3×C7×D4×D7, C3×C7×#1159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 274);