Finite Group DatabasebetaFinite Group Databasebeta| order | 1272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C53 ⋊ D4 |
| Sylow | C53 ⋊ D12 |
| Sylow | C3 ⋊ C22⋊D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D53 |
| commutator, Fitting, socle, cosocle | C2×C3×C53 | C22 |
| hypocenter | C3×C53 | D4 |
| LCS | G ▷ C2×C3×C53 ▷ C3×C53 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 60 |
| transitive degree | μt(G) = 636 |
Polycyclic presentation:
2^3,3,53|a^2=c,b^a=bc,e^a=e^52,d^b=d^2165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1272, 12);