Finite Group DatabasebetaFinite Group Databasebeta| order | 10900 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C109 · Schur multiplier (H2) = C5 |
| direct product | #1039×C109 |
| derived, Sylow | C52 ⋊ C4×C109 |
| Hall | C52×C109 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C109 | C5⋊D5 |
| commutator, hypocenter | C52 | C4×C109 |
| Frattini | C2 | C5⋊D5×C109 |
| Fitting, socle, prime radical | C2×C52×C109 | C2 |
| cosocle | C2×C52 | C2×C109 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C109 | |
48 conjugacy classes of subgroups.
3052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1039×C109⋊C3, C109×#1039⋊C3, #1039⋊(C109⋊C3), … |
| maximal normal subgroup of | #1039×C109⋊C3, C109×#1039⋊C3, #1039⋊(C109⋊C3), … |
| maximal quotient of | C109×C3⋊#1039, C3×#1039×C109 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10900, 20);