Finite Group DatabasebetaFinite Group Databasebeta| order | 1104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D12×D23 |
| Fitting | C3×C4×C23 ⋊ C22 |
| Hall | C3×C23 ⋊ C2×D4 |
| Sylow | C23 ⋊ C2×D12 |
| Sylow | C3 ⋊ D4×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D23 |
| commutator, socle, cosocle | C2×C3×C23 | C23 |
| Fitting | C3×C4×C23 | C22 |
| hypercenter | C4 | D3×D23 |
| hypocenter | C3×C23 | C2×D4 |
| LCS | G ▷ C2×C3×C23 ▷ C3×C23 | |
| UCS | C1 ◁ C2 ◁ C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 276 |
117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1104, 107);