Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Fitting | C7×#2840 ⋊ C2 |
| Sylow | C7 ⋊ #36675 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2840 | C2 |
| hypercenter | #2840 | D7 |
| hypocenter | C7 | #36675 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|e^2=g,b^a=bf,c^a=cg,d^a=dh,i^a=i^6,c^b=ch,d^c=dfh,i^c=i^6,i^e=i^6130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 376001);