Finite Group DatabasebetaFinite Group Databasebeta| order | 1044 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D29 |
| unambiguous semidirect product | C29⋊(C22×C32) |
| unambiguous semidirect product | (C2×C29)⋊(C2×C32) |
| Fitting, socle | C2×C32×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C22×C32 |
| Hall | C32×C29 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D29 |
| commutator, cosocle, hypocenter | C29 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 522 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D11×D29, C2×C32×D319, C2×C32×C11×D29, … |
| maximal normal subgroup of | C2×C32×C11×D29, C2×C32×C13×D29, C2×C32×C17×D29, … |
| maximal quotient of | C32×D11×D29, C2×C32×D319, C2×C32×C11×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1044, 31);