Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×#92150⋊C5 |
| unambiguous semidirect product | #92150⋊C52 |
| unambiguous semidirect product | (C5×#92150)⋊C5 |
| Fitting, socle | C5×C112 ⋊ C4×C5 |
| derived, Sylow | C112 ⋊ C4×C52 |
| Hall | C5×#10597243 ⋊ C4 |
| Hall | #92150 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #92150⋊C5 |
| commutator, hypocenter | C112 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112 | C4×C5 |
| prime radical | C5×#11925892 | C2 |
| cosocle | C11⋊D11 | C2×C52 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C5 | |
144 conjugacy classes of subgroups.
130 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#13089721⋊C5, C5×(#92150⋊C3)⋊C5, C3×C5×#92150⋊C5, … |
| maximal normal subgroup of | C5×(#92150⋊C3)⋊C5, C3×C5×#92150⋊C5 |
| maximal quotient of | C3×C5×#92150⋊C5, C5×C3⋊(#92150⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 169);