Finite Group DatabasebetaFinite Group Databasebeta| order | 10374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#19104441 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19104441 |
| commutator, cosocle, hypocenter | C7×C13×C19 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C13×C19 | C3 |
| LCS | G ▷ C7×C13×C19 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
1158 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19104441, #35208811, #35208824, … |
| maximal normal subgroup of | C4×#19104441, #35208811, #35208824, … |
| maximal quotient of | C4×#19104441, C22×#19104441, C2×#29509842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10374, 11);