Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C61×#418 ⋊ C2 |
| Sylow | C61 ⋊ #1910 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16839638 |
| commutator | C2×C4×C61 | C22×C4 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#418 | C2 |
| socle | C2×C61 | #386 |
| hypercenter | #418 | D61 |
| hypocenter | C61 | #1910 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #418 | |
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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=dfg,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,e^b=eg,d^c=dg,f^c=fg,h^c=h^60689 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1910, C2×#21446343, #29681995, … |
| maximal normal subgroup of | D61×#1910, C2×#21446343, #29681995, … |
| maximal quotient of | #29575515, #29575520, #29575535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5034);