Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C32×C7 ⋊ #41 |
| Sylow | C32 ⋊ #1159 |
| Sylow | C7 ⋊ #3795 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×D7 |
| commutator, Fitting, socle, cosocle | C2×C32×C7 | C23 |
| hypocenter | C32×C7 | #41 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C2 | |
172 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^4,3^2,7|a^2=d,c^a=cd,g^a=g^6,c^b=cd,e^b=e^2,f^c=f^272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 618);