Finite Group DatabasebetaFinite Group Databasebeta| order | 1904 |
| isoclinism | isoclinic class of C7⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C7×C17 ⋊ C2×C8 |
| Sylow | C17 ⋊ C2×C7⋊C8 |
| Sylow | C7 ⋊ #63242 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C7⋊#595 |
| commutator, hypocenter | C7×C17 | C2×C8 |
| Frattini | C2 | C2×C7⋊#595 |
| Fitting | C4×C7×C17 | C4 |
| socle | C2×C7×C17 | C2×C4 |
| prime radical | C2×C7×D17 | C4 |
| cosocle | C7×Dic17 | C22 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 952 |
Polycyclic presentation:
2^4,7,17|a^2=c,b^2=d,c^2=d,e^a=e^6,f^a=f^13,f^c=f^16152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1904, 104);