Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #2102 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14519763 |
| commutator | C22×C4×C61 | C23 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#344 | C2 |
| socle | C2×C61 | #400 |
| hypercenter | #344 | D61 |
| hypocenter | C61 | #2102 |
| LCS | G ▷ C22×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #344 | |
158 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^2=de,c^2=d,d^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^60,c^b=cf,d^b=dg,e^b=eg,f^c=fg686 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2102, C2×#21447396, #29709982, … |
| maximal normal subgroup of | D61×#2102, C2×#21447396, #29709982, … |
| maximal quotient of | #29585140, #29585145, #29585150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6087);