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 | #15690028 ⋊ C2 |
| Hall | C11⋊D11 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | #11925894 |
| commutator, hypocenter | C112 | C2×C25 |
| Fitting, socle | C5×C112 | C2×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11^2,5|b^5=e,c^a=c^10,d^a=d^10,c^b=c^9,d^b=d^4110 conjugacy classes — view the full character table.
| maximal subgroup of | #20258404⋊C2, C2×#20258404, C3×#20258404, … |
| maximal normal subgroup of | #20258404⋊C2, C2×#20258404, C3×#20258404 |
| maximal quotient of | #27130778, C2×#20258404, C3×#20258404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6050, 22);