Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Sylow | C7 ⋊ #14663 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C23×C7 | C23×C4 |
| Fitting | C7×#1446 | C2 |
| socle, prime radical, cosocle | C24×C7 | C24 |
| hypercenter | #1446 | D7 |
| hypocenter | C7 | #14663 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ #1446 | |
1462 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1462 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1792 |
Polycyclic presentation:
2^8,7|a^2=f,b^2=h,c^2=e,d^2=e,b^a=be,c^a=cf,i^a=i^6,c^b=cg,d^b=def,d^c=de184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 100616);