Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C11 |
| direct product | C5×D5×C11⋊D11 |
| Fitting, socle, Hall | C52×C112 ⋊ C22 |
| derived | C5×C112 ⋊ C22×C5 |
| Sylow | C112 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×C11⋊D11 |
| commutator, cosocle, hypocenter | C5×C112 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C22 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C5 | |
336 conjugacy classes of subgroups.
1240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 249);