Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×#11925890 |
| Fitting, socle | C5×C112 ⋊ C2×D5 |
| derived, Hall | C5×#10597245 ⋊ C22 |
| Sylow | C112 ⋊ D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#10597245 | C22 |
| Fitting, socle | C5×C112 | C2×D5 |
| LCS | G ▷ C5×#10597245 | |
| UCS | C1 | |
78 conjugacy classes of subgroups.
124 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#11925890, D15×#11925890, D5×C3⋊#11925890, … |
| maximal normal subgroup of | C3×D5×#11925890 |
| maximal quotient of | C3×D5×#11925890, D15×#11925890, D5×C3⋊#11925890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 209);