Finite Group DatabasebetaFinite Group Databasebeta| order | 1104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#237 |
| Fitting | C3×D4×C23 ⋊ C2 |
| Hall | C3×C23 ⋊ #41 |
| Sylow | C3 ⋊ #41×C23 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C23 | C22×D3 |
| commutator, cosocle | C2×C3 | C23×C23 |
| Frattini | C2 | C22×D3×C23 |
| Fitting | C3×D4×C23 | C2 |
| socle | C2×C3×C23 | C23 |
| hypercenter | D4×C23 | D3 |
| hypocenter | C3 | #41×C23 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C23 ◁ D4×C23 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 552 |
345 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1104, 141);