Finite Group DatabasebetaFinite Group Databasebeta| order | 8145 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C3×C42×C5×C9 (order 4320) · Inn(G) = C1 · Out(G) = C2×C3×C42×C5×C9 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8145 |
| abelian | C5×C9×C181 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C3 | C3×C5×C181 |
| socle | C3×C5×C181 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
8145 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C9×C181, C5×C9×D181, C9×D5×C181, … |
| maximal normal subgroup of | C2×C5×C9×C181, C5×C9×D181, C9×D5×C181, … |
| maximal quotient of | C2×C5×C9×C181, C5×C22⋊C9×C181, C5×C27×C181, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8145, 1);