Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #92688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#92691 |
| Hall | C32×C7 ⋊ C2×Q8 |
| Sylow | C32 ⋊ C2×Dic14 |
| Sylow | C7 ⋊ C2×#627 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D21 |
| commutator, cosocle | C2×C32×C7 | C23 |
| Frattini | C2 | C2×D3×D21 |
| Fitting, socle, prime radical | C22×C32×C7 | C22 |
| hypocenter | C32×C7 | C2×Q8 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 | |
168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 794);