Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D545 |
| unambiguous semidirect product | (C5×D5)⋊D109 |
| unambiguous semidirect product | (D5×C109)⋊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.
1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3874⋊D109, D5×C5⋊(D109⋊C3), C3×D5×D545, … |
| maximal normal subgroup of | D5×C5⋊(D109⋊C3), C3×D5×D545 |
| maximal quotient of | C3×D5×D545, D5×D1635, D15×D545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 44);