Finite Group DatabasebetaFinite Group Databasebeta| order | 1264 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D79)⋊C4 |
| Fitting | C2×C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D79 |
| commutator | C2×C79 | C2×C4 |
| Fitting | C2×C4×C79 | C2 |
| socle, cosocle | C22×C79 | C22 |
| prime radical | C22×D79 | C2 |
| hypercenter | C2×C4 | D79 |
| hypocenter | C79 | C22⋊C4 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 632 |
Polycyclic presentation:
2^4,79|a^2=d,b^a=bc,e^b=e^78322 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D79, C2×(C2×D79)⋊C4, #14579118, … |
| maximal normal subgroup of | C22⋊C4×D79, C2×(C2×D79)⋊C4, #14579118, … |
| maximal quotient of | C79⋊#95, (C2×D79)⋊C8, #14579075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1264, 17);