Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C72×C37 ⋊ C2×C32 |
| derived | C7×C37 ⋊ C2×C32×C7 |
| Hall | C7×ΓL(1,𝔽8)×C37⋊C3 ⋊ C2 |
| Hall | C72×D37 ⋊ C32 |
| Hall | D37 ⋊ C3×C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C3×D37⋊C3 |
| Sylow | C37 ⋊ C2×C3×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | ΓL(1,𝔽8)×D37⋊C3 |
| commutator, cosocle, hypocenter | C7×C37 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C2×C32 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C7 | |
112 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 777 |
420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 173);