Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | Aut(G) order 13444704 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5187 |
| unambiguous semidirect product | C3⋊D1729 |
| unambiguous semidirect product | C7⋊D741 |
| unambiguous semidirect product | C13⋊D399 |
| unambiguous semidirect product | C19⋊D273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C13×C19 | C2 |
| LCS | G ▷ C3×C7×C13×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,13,19|b^a=b^2,c^a=c^6,d^a=d^12,e^a=e^182595 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D273, D13×D399, D21×D247, … |
| maximal normal subgroup of | D19×D273, D13×D399, D21×D247, … |
| maximal quotient of | Dic5187, C2×D5187, D15561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 29);