Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1798 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | C2×#117×C61 | C2 |
| hypercenter | C2×#117 | D61 |
| hypocenter | C61 | #1798 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
312 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 125 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=f,b^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^60,c^b=cg1244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29567139, #29567140, #29567142, … |
| maximal normal subgroup of | #29567139, #29567140, #29567142, … |
| maximal quotient of | #29572686, #29572691, #29572716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4494);