Finite Group DatabasebetaFinite Group Databasebeta| order | 1264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D79 |
| commutator, socle, cosocle | C2×C79 | C23 |
| Frattini | C2 | C22×D79 |
| Fitting | C2×C4×C79 | C2 |
| hypercenter | C2×C4 | D79 |
| hypocenter | C79 | #41 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 632 |
Polycyclic presentation:
2^4,79|c^2=d,b^a=bd,e^b=e^78322 conjugacy classes — view the full character table.
| maximal subgroup of | #14579087, #14579089, #14579167, … |
| maximal normal subgroup of | #14579087, #14579089, #14579167, … |
| maximal quotient of | #14579118, #14579120, C4×C22⋊D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1264, 40);