Finite Group DatabasebetaFinite Group Databasebeta| order | 1176 |
| isoclinism | isoclinic class of D21⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C3×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ #87639 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D21⋊D7 |
| commutator, hypocenter | C3×C72 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C72 | C22 |
| prime radical | C2×C3×C7⋊D7 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
Polycyclic presentation:
2^3,3,7^2|a^2=c,d^a=d^2,e^a=e^6,e^b=e^6,f^b=f^6102 conjugacy classes — view the full character table.
| maximal subgroup of | #72222056, D3×#87639, #72222120, … |
| maximal normal subgroup of | #72222056, D3×#87639, #72222120, … |
| maximal quotient of | C3×#11924252, C2×#11924252, #72254195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1176, 167);