Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C61×#578 ⋊ C2 |
| Sylow | C61 ⋊ #3293 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×C22⋊D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#578 | C2 |
| socle | C2×C61 | D42 |
| hypercenter | #578 | D61 |
| hypocenter | C61 | #3293 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #578 | |
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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=g,b^2=g,c^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,f^c=fg,h^c=h^60,e^d=eg689 conjugacy classes — view the full character table.
| maximal subgroup of | #29836767, #29836768, #29836774, … |
| maximal normal subgroup of | #29836767, #29836768, #29836774, … |
| maximal quotient of | #29671320, #29671322, #29671326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 16312);