Finite Group DatabasebetaFinite Group Databasebeta| order | 15974 |
| isoclinism | isoclinic class of D163 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D163 |
| unambiguous semidirect product | C163⋊(C2×C72) |
| Fitting, socle, Hall | C72×C163 ⋊ C2 |
| derived, Sylow | C163 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D163 |
| commutator, cosocle, hypocenter | C163 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C163 | C2 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7987 |
4067 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D163, C7⋊D7×D163, C2×C72×D163 |
| maximal normal subgroup of | C7×D7×D163, C7⋊D7×D163, C2×C72×D163 |
| maximal quotient of | C72×Dic163, C2×C72×D163 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15974, 10);