Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×#322 ⋊ C2 |
| Sylow | C61 ⋊ SD16⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D244 |
| commutator | C4×C61 | C22×C8 |
| Frattini | C42 | C22×D61 |
| Fitting | C61×#322 | C2 |
| socle | C22×C61 | C4×D4 |
| hypercenter | #322 | D61 |
| hypocenter | C61 | SD16⋊C8 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 ◁ #322 | |
176 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 176 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,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^60,d^b=df,h^b=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×SD16⋊C8, C2×#21444633, #29649414, … |
| maximal normal subgroup of | D61×SD16⋊C8, C2×#21444633, #29649414, … |
| maximal quotient of | #29570791, #29570798, #29571262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3324);