Finite Group DatabasebetaFinite Group Databasebeta| order | 2156 |
| isoclinism | isoclinic class of (C7⋊D7)⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C7⋊D7)⋊D11 |
| unambiguous semidirect product | D77⋊D7 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C22 |
| Sylow | C72 ⋊ C2×D11 |
| Sylow | C11 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11 | C22 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 154 |
Polycyclic presentation:
2^2,7^2,11|c^a=c^6,e^a=e^10,c^b=c^6,d^b=d^6155 conjugacy classes — view the full character table.
| maximal subgroup of | (C7⋊D7)⋊D121, C11×(C7⋊D7)⋊D11, D77⋊D77, … |
| maximal normal subgroup of | C11×(C7⋊D7)⋊D11, C13×(C7⋊D7)⋊D11, C17×(C7⋊D7)⋊D11, … |
| maximal quotient of | (C7⋊D7)⋊D121, C11×(C7⋊D7)⋊D11, D77⋊D77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2156, 21);