Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#408 ⋊ C2 |
| Sylow | C61 ⋊ #2017 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14519773 |
| commutator | C22×C4×C61 | C23 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#408 | C2 |
| socle | C2×C61 | #392 |
| hypercenter | #408 | D61 |
| hypocenter | C61 | #2017 |
| LCS | G ▷ C22×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #408 | |
350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,f^b=fg,h^b=h^60,e^c=eg,f^c=fg,h^c=h^60866 conjugacy classes — view the full character table.
| maximal subgroup of | #29567531, #29567533, #29567534, … |
| maximal normal subgroup of | #29567531, #29567533, #29567534, … |
| maximal quotient of | #29580612, #29580613, #29580617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5614);