Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C61 ⋊ C8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | #95×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | #95 | #6923 |
| hypocenter | C61 | C8×C4⋊C4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #95 | |
296 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 134 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=de,e^2=g,b^a=bd,h^a=h^50,h^c=h^11,h^e=h^60380 conjugacy classes — view the full character table.
| maximal subgroup of | #30597910, #30597915, #30597940, … |
| maximal normal subgroup of | #30597910, #30597915, #30597940, … |
| maximal quotient of | #30597950, #30597959, #30597973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20302);