Finite Group DatabasebetaFinite Group Databasebeta| order | 8804 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic71 |
| unambiguous semidirect product | C71⋊(C4×C31) |
| derived, Sylow | C71 ⋊ C4×C31 |
| Hall | C31×C71 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D71 |
| commutator, hypocenter | C71 | C4×C31 |
| Frattini | C2 | C31×D71 |
| Fitting, socle | C2×C31×C71 | C2 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C31 | |
12 conjugacy classes of subgroups.
2294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C31×Dic71, C31×Dic213, C31⋊C3×Dic71 |
| maximal normal subgroup of | C3×C31×Dic71, C31⋊C3×Dic71 |
| maximal quotient of | C3×C31×Dic71, C31×Dic213 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8804, 3);