Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1996 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊C4×D61 |
| commutator | C23×C61 | C22×C4 |
| Frattini | C24 | C22×D61 |
| Fitting | C61×#342 | C2 |
| socle | C22×C61 | C2×C22⋊C4 |
| hypercenter | #342 | D61 |
| hypocenter | C61 | #1996 |
| LCS | G ▷ C23×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^c=h^60692 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1996, C2×#21446802, #29684655, … |
| maximal normal subgroup of | D61×#1996, C2×#21446802, #29684655, … |
| maximal quotient of | #29580050, #29580054, #29580058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5493);