Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | D5×C11×D55 |
| unambiguous semidirect product | (C5×D5)⋊(C11×D11) |
| unambiguous semidirect product | (D5×C11)⋊(D5×C11) |
| Fitting, socle, Hall | C52×C112 ⋊ C22 |
| derived | C52×C11 ⋊ C22×C11 |
| Sylow | C112 ⋊ D52 |
| Sylow | C52 ⋊ C2×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D5×D55 |
| commutator, cosocle, hypocenter | C52×C11 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C22 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C11 | |
146 conjugacy classes of subgroups.
1276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#3874⋊D11, D5×C5⋊#10624391, C3×D5×C11×D55, … |
| maximal normal subgroup of | C3×D5×C11×D55 |
| maximal quotient of | C3×D5×C11×D55, D5×C11×D165, C11×D15×D55, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 271);