Finite Group DatabasebetaFinite Group Databasebeta| order | 2156 |
| isoclinism | isoclinic class of D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D72 |
| unambiguous semidirect product | (C7×D7)⋊(C2×C11) |
| unambiguous semidirect product | (C7⋊D7)⋊(C2×C11) |
| Fitting, socle, Hall | C72×C11 ⋊ C22 |
| derived, Sylow | C72 ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D72 |
| commutator, cosocle, hypocenter | C72 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D72×C121, C112×D72, C11×D7×D77, … |
| maximal normal subgroup of | D72×C121, C112×D72, C11×C13×D72, … |
| maximal quotient of | D72×C121, C112×D72, C11×D7×D77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2156, 19);