Finite Group DatabasebetaFinite Group Databasebeta| order | 1104 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D69 |
| Fitting | C2×C3×C4×C23 ⋊ C2 |
| derived, Hall | C3×C23 ⋊ C22×C4 |
| Sylow | C23 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D69 |
| commutator, hypocenter | C3×C23 | C22×C4 |
| Frattini | C2 | C22×D69 |
| Fitting | C2×C3×C4×C23 | C2 |
| socle | C22×C3×C23 | C22 |
| prime radical | C22×D69 | C2 |
| cosocle | C2×C3×C23 | C23 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1104, 147);