Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C21780 |
| abelian | C4×C5×C9×C121 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C11 | C2×C3×C5×C11 |
| socle, prime radical | C2×C3×C5×C11 | C2×C3×C11 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
54 conjugacy classes of subgroups.
21780 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic10890, D21780 |
| maximal subgroup of | Dic10890, D21780 |
| maximal normal subgroup of | Dic10890, D21780 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 1);