Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #10620796 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | C24×C7 ⋊ C3×C4 |
| Hall | #90019 ⋊ C3 |
| Sylow | C7 ⋊ #379⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10620796 |
| commutator, hypocenter | C24×C7 | C3×C4 |
| Frattini | C23 | A4×D7 |
| Fitting, cosocle | C25×C7 | C2×C3 |
| socle | C23×C7 | C2×A4 |
| prime radical | C2×C7×C22⋊A4 | C2 |
| LCS | G ▷ C24×C7 | |
| UCS | C1 ◁ C2 | |
212 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
Polycyclic presentation:
2,3,2^5,7|a^2=c,d^a=df,e^a=efg,h^a=h^6,d^b=de,e^b=d,f^b=g,g^b=fg68 conjugacy classes — view the full character table.
| maximal subgroup of | #72276787, #72277266, #72277737, … |
| maximal normal subgroup of | #72276787, #72277266, #72277737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1453);