Finite Group DatabasebetaFinite Group Databasebeta| order | 1264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D79 |
| commutator, cosocle | C4×C79 | C22 |
| Frattini | C4 | C2×D79 |
| Fitting | Q8×C79 | C2 |
| socle, prime radical | C2×C79 | D4 |
| hypercenter | Q8 | D79 |
| hypocenter | C79 | Q16 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 1264 |
Polycyclic presentation:
2^4,79|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^78202 conjugacy classes — view the full character table.
| maximal subgroup of | Q16×D79, C2×#11929614, #14579181, … |
| maximal normal subgroup of | Q16×D79, C2×#11929614, #14579181, … |
| maximal quotient of | #14579084, #14579085, #14579094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1264, 30);