Finite Group DatabasebetaFinite Group Databasebeta| order | 17444 |
| isoclinism | isoclinic class of C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C89 · Schur multiplier (H2) = C7 |
| direct product | C89×C7⋊Dic7 |
| unambiguous semidirect product | C7⋊(Dic7×C89) |
| derived, Sylow | C72 ⋊ C4×C89 |
| Hall | C72×C89 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C89 | C7⋊D7 |
| commutator, hypocenter | C72 | C4×C89 |
| Frattini | C2 | C89×C7⋊D7 |
| Fitting, socle, prime radical | C2×C72×C89 | C2 |
| cosocle | C2×C72 | C2×C89 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C89 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17444 |
4628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17444, 16);