Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×Q8⋊C8 ⋊ C2 |
| Sylow | C61 ⋊ C8×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D61 |
| commutator | C4×C61 | C22×C8 |
| Frattini | C42 | C22×D61 |
| Fitting | C61×Q8⋊C8 | C2 |
| socle | C22×C61 | C4×D4 |
| hypercenter | Q8⋊C8 | D61 |
| hypocenter | C61 | C8×SD16 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8 | |
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^c=h^60896 conjugacy classes — view the full character table.
| maximal subgroup of | C8×SD16×D61, C2×#21444616, #29649387, … |
| maximal normal subgroup of | C8×SD16×D61, C2×#21444616, #29649387, … |
| maximal quotient of | #29570776, #29570787, #29571236, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3307);