Finite Group DatabasebetaFinite Group Databasebeta| order | 6050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C112 ⋊ C2×C25 |
| Hall | #15690029 ⋊ C2 |
| Hall | C11×D11 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #11925896 |
| commutator, hypocenter | C112 | C2×C25 |
| Fitting, socle | C5×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C5 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11^2,5|b^5=e,c^a=c^10,c^b=c^3,d^b=d^4125 conjugacy classes — view the full character table.
| maximal subgroup of | #20258406⋊C2, C2×#20258406, C3×#20258406, … |
| maximal normal subgroup of | #20258406⋊C2, C2×#20258406, C3×#20258406 |
| maximal quotient of | #27130780, C2×#20258406, C3×#20258406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 24);