Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #1752 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator | C22×C61 | C2×C42 |
| Fitting | C23×C8×C61 | C2 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C23×C8 | D61 |
| hypocenter | C61 | #1752 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C8 | |
360 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 157 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,e^2=g,b^a=bd,c^b=cg,h^b=h^601976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29566998, #29566999, #29567001, … |
| maximal normal subgroup of | #29566998, #29566999, #29567001, … |
| maximal quotient of | #29570482, #29570486, #29570508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4286);