Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1454 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C2×C42 |
| Fitting | C4⋊C8×C61 | C4 |
| hypercenter | C4⋊C8 | #6923 |
| hypocenter | C61 | #1454 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
178 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 78 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=e,d^2=f,e^2=g,c^a=cfg,h^a=h^11,c^b=cf,h^c=h^60,h^d=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | D61⋊#1454, C2×#21461041, #30609736, … |
| maximal normal subgroup of | D61⋊#1454, C2×#21461041, #30609736, … |
| maximal quotient of | #30595977, #30595999, #30597385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19732);