Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C61×#339 ⋊ C2 |
| Sylow | C61 ⋊ #1764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D61 |
| commutator | C4×C61 | C2×C42 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#339 | C2 |
| socle | C22×C61 | C4×D4 |
| hypercenter | #339 | D61 |
| hypocenter | C61 | #1764 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #339 | |
300 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 105 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=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^60896 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1764, C2×#21445653, #29677856, … |
| maximal normal subgroup of | D61×#1764, C2×#21445653, #29677856, … |
| maximal quotient of | #29570684, #29570694, #29570701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4344);