Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊D109 |
| unambiguous semidirect product | D545⋊D5 |
| Fitting, socle, derived, Hall | C52×C109 ⋊ C22 |
| Sylow | C109 ⋊ D52 |
| Sylow | C52 ⋊ C2×D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C109 | C22 |
| LCS | G ▷ C52×C109 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,109|c^a=c^4,e^a=e^108,c^b=c^4,d^b=d^4772 conjugacy classes — view the full character table.
| maximal subgroup of | ((C5⋊D5)⋊C3)⋊D109, (C5⋊(D109⋊C3))⋊D5, C3×(C5⋊D5)⋊D109, … |
| maximal normal subgroup of | (C5⋊(D109⋊C3))⋊D5, C3×(C5⋊D5)⋊D109 |
| maximal quotient of | C3×(C5⋊D5)⋊D109, D545⋊D15, #45658348 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 45);