Finite Group DatabasebetaFinite Group Databasebeta| order | 10196 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C2549 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2549 | C4 |
| prime radical, cosocle | D2549 | C2 |
| LCS | G ▷ C2549 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,2549|a^2=b,c^a=c^357,c^b=c^2548641 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23779237, C3×#23779237, C3⋊#23779237 |
| maximal normal subgroup of | C2×#23779237, C3×#23779237 |
| maximal quotient of | #35205157, C2×#23779237, C3×#23779237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10196, 3);