Finite Group DatabasebetaFinite Group Databasebeta| order | 10004 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×Dic41 |
| derived, Sylow | C41 ⋊ C4×C61 |
| Hall | C41×C61 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C61 | D41 |
| commutator, hypocenter | C41 | C4×C61 |
| Frattini | C2 | C61×D41 |
| Fitting, socle, prime radical | C2×C41×C61 | C2 |
| cosocle | C2×C41 | C2×C61 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C61 | |
12 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C61×Dic41, C61×Dic123, Dic41×C61⋊C3 |
| maximal normal subgroup of | C3×C61×Dic41, Dic41×C61⋊C3 |
| maximal quotient of | C3×C61×Dic41, C61×Dic123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10004, 2);