Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C11 |
| direct product | Dic5×C112⋊C9 |
| unambiguous semidirect product | (C112×Dic5)⋊C9 |
| derived, Hall | C5×C112 ⋊ C4×C9 |
| Hall | C5×C112⋊C9 ⋊ C4 |
| Hall | C112×Dic5 ⋊ C9 |
| Sylow | C112 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ C4×C112⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D5×C112⋊C3 |
| commutator, hypocenter | C5×C112 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C112 | C2×C3 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C2×C3 | |
84 conjugacy classes of subgroups.
1032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 153);