Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D55⋊D55 |
| Fitting, socle, derived, Hall | C52×C112 ⋊ C22 |
| Sylow | C112 ⋊ D52 |
| Sylow | C52 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C112 | C22 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,11^2|d^a=d^4,e^a=e^10,f^a=f^10,c^b=c^4,f^b=f^10811 conjugacy classes — view the full character table.
| maximal subgroup of | #49137581, #49137609, C3×D55⋊D55, … |
| maximal normal subgroup of | C3×D55⋊D55 |
| maximal quotient of | C3×D55⋊D55, #49137774, D55⋊D165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 276);