Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C13×C19 | C2×C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,13,19|c^a=c^6,d^a=d^12,e^a=e^18,c^b=c^2,d^b=d^9318 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#10587723, #10587717⋊D19, #10587721⋊D19, … |
| maximal normal subgroup of | D19×#10587723, #10587717⋊D19, #10587721⋊D19, … |
| maximal quotient of | #35208890, C2×#23780627, #44527635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 118);