Finite Group DatabasebetaFinite Group Databasebeta| order | 8970 |
| automorphism | Aut(G) order 9472320 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4485 |
| unambiguous semidirect product | C3⋊D1495 |
| unambiguous semidirect product | C5⋊D897 |
| unambiguous semidirect product | C13⋊D345 |
| unambiguous semidirect product | C23⋊D195 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C13×C23 | C2 |
| LCS | G ▷ C3×C5×C13×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,13,23|b^a=b^2,c^a=c^4,d^a=d^12,e^a=e^222244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D195, D13×D345, D15×D299, … |
| maximal normal subgroup of | D23×D195, D13×D345, D15×D299, … |
| maximal quotient of | Dic4485, C2×D4485, D13455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8970, 17);