Finite Group DatabasebetaFinite Group Databasebeta| order | 8004 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×C29×Dic23 |
| unambiguous semidirect product | C23⋊(C3×C4×C29) |
| derived, Sylow | C23 ⋊ C3×C4×C29 |
| Hall | C3×C23×C29 ⋊ C4 |
| Hall | C23×C29 ⋊ C3×C4 |
| Hall | C3×C23 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C29 | D23 |
| commutator, hypocenter | C23 | C3×C4×C29 |
| Frattini | C2 | C3×C29×D23 |
| Fitting, socle | C2×C3×C23×C29 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C3×C29 | |
24 conjugacy classes of subgroups.
2262 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C29×Dic23, C3×C29×Dic69, C32×C29×Dic23 |
| maximal normal subgroup of | C9×C29×Dic23, C32×C29×Dic23 |
| maximal quotient of | C9×C29×Dic23, C3×C29×Dic69, C32×C29×Dic23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8004, 3);