Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | SL(2,𝔽7) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, socle, hypercenter | C22 | SO(3,𝔽7) |
| commutator, hypocenter | SL(2,𝔽7) | C4 |
| prime radical, cosocle | C2×SL(2,𝔽7) | C2 |
| LCS | G ▷ SL(2,𝔽7) | |
| UCS | C1 ◁ C22 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
Permutation generators:
(1,5,11,6,3,15,13,9,16,12,7,8,4,2)(10,14)(17,18)(19,20);(1,15,10,5,2,11,6,8,9,4,14,16,13,12,7,3)(17,20,18,19)32 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13057024, C4×#10621462 |
| maximal normal subgroup of | C3×#13057024, C4×#10621462 |
| maximal quotient of | C3×#13057024 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6313);