Finite Group DatabasebetaFinite Group Databasebeta| order | 10004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C41×C61 ⋊ C4 |
| Sylow | C61 ⋊ #4223 |
| Sylow | C41 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C61 | C4 |
| prime radical, cosocle | D2501 | C2 |
| LCS | G ▷ C41×C61 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,41,61|a^2=b,c^a=c^32,d^a=d^50,c^b=c^40,d^b=d^60629 conjugacy classes — view the full character table.
| maximal subgroup of | #23756302⋊C3, C3×#23756302, C3⋊#23756302 |
| maximal normal subgroup of | #23756302⋊C3, C3×#23756302 |
| maximal quotient of | C3×#23756302, C3⋊#23756302 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10004, 8);