Finite Group DatabasebetaFinite Group Databasebeta| order | 10484 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2621 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2621 | C4 |
| prime radical, cosocle | D2621 | C2 |
| LCS | G ▷ C2621 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,2621|a^2=b,c^a=c^472,c^b=c^2620659 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23783157, C3×#23783157, C3⋊#23783157 |
| maximal normal subgroup of | C2×#23783157, C3×#23783157 |
| maximal quotient of | #35230440, C2×#23783157, C3×#23783157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10484, 3);