Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #89912 ⋊ C3 |
| Sylow | C7 ⋊ #504⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | A4×D7 |
| commutator, hypocenter | C7×Q8 | C3×C8 |
| Fitting, cosocle | C7×#131 | C2×C3 |
| socle | C2×C7 | C8×A4 |
| prime radical | C7×#41⋊C3 | C4 |
| LCS | G ▷ C7×Q8 | |
| UCS | C1 ◁ C8 | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2,3,2^4,7,2|a^2=c,c^2=d,d^2=h,e^2=h,f^2=h,g^a=g^6,e^b=ef,f^b=e,f^e=fh140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1448);