Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D21⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D21⋊D7 |
| Fitting, socle | C2×C3×C72 ⋊ C22 |
| derived, Hall | C3×C72 ⋊ C23 |
| Sylow | C72 ⋊ C22×D3 |
| Sylow | C3 ⋊ C2×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D21⋊D7 |
| commutator, cosocle, hypocenter | C3×C72 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72 | C22 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13183634, #72222113, #72222120, … |
| maximal normal subgroup of | C2×#13183634, #72222113, #72222120, … |
| maximal quotient of | #72222120, D3×D21⋊D7, C2×C3×D21⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 266);