Finite Group DatabasebetaFinite Group Databasebeta| order | 8804 |
| automorphism | Aut(G) order 9244200 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4402 |
| direct product | C2×D2201 |
| unambiguous semidirect product | (C2×C31)⋊D71 |
| unambiguous semidirect product | (C2×C71)⋊D31 |
| Fitting, socle | C2×C31×C71 ⋊ C2 |
| derived, Hall | C31×C71 ⋊ C22 |
| Sylow | C71 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2201 |
| commutator, hypocenter | C31×C71 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C71 | C2 |
| LCS | G ▷ C31×C71 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C71⋊(D31⋊C3), D3×D2201, C2×C3×D2201, … |
| maximal normal subgroup of | C2×C71⋊(D31⋊C3), C2×C3×D2201, D8804 |
| maximal quotient of | D3×D2201, C2×C3×D2201, C2×D6603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8804, 7);