Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1770 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C22×C61 | C2×C42 |
| Fitting | #95×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | #95 | #6923 |
| hypocenter | C61 | #1770 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #95 | |
272 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 114 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^11,c^b=cg,h^c=h^11,h^e=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | #30597920, #30597925, #30597930, … |
| maximal normal subgroup of | #30597920, #30597925, #30597930, … |
| maximal quotient of | #30597952, #30597957, #30597976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20305);