Finite Group DatabasebetaFinite Group Databasebeta| order | 19404 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| derived, Hall | C72×C11 ⋊ C32×C4 |
| Hall | C11×ΓL(1,𝔽8)2 ⋊ C4 |
| Hall | C7⋊Dic77 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ Dic11 |
| Sylow | C72 ⋊ C32×Dic11 |
| Sylow | C11 ⋊ ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽7)) |
| commutator, hypocenter | C72×C11 | C32×C4 |
| Fitting, socle, cosocle | C2×C72×C11 | C2×C32 |
| prime radical | C2×C11×ΓL(1,𝔽8)2 | C2 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 924 |
Polycyclic presentation:
2,3^2,7^2,11,2|a^2=g,d^a=d^6,e^a=e^6,f^a=f^10,d^b=d^2,e^c=e^2302 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19404, 238);