Finite Group DatabasebetaFinite Group Databasebeta| order | 1272 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×D53 |
| unambiguous semidirect product | C53⋊(C23×C3) |
| unambiguous semidirect product | (C2×C53)⋊(C22×C3) |
| Fitting, socle | C22×C3×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C23×C3 |
| Hall | C3×C53 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D53 |
| commutator, cosocle, hypocenter | C53 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 636 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1272, 41);