Finite Group DatabasebetaFinite Group Databasebeta| order | 22155 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C32×C4×C5×C7 (order 10080) · Inn(G) = C1 · Out(G) = C23×C32×C4×C5×C7 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C22155 |
| abelian | C3×C5×C7×C211 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
16 conjugacy classes of subgroups.
22155 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C5×C7×C211, C3×C5×C7×D211, C3×C5×D7×C211, … |
| maximal normal subgroup of | C2×C3×C5×C7×C211, C3×C5×C7×D211, C3×C5×D7×C211, … |
| maximal quotient of | C2×C3×C5×C7×C211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22155, 1);