Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C22⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C22×C61 | C2×C42 |
| Fitting | C2×C22⋊C4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C2×C22⋊C4 | #6923 |
| hypocenter | C61 | C22⋊#95 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
1088 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 202 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=g,b^a=bd,c^a=ce,h^b=h^11,h^g=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | #30594338, #30602455, #30602456, … |
| maximal normal subgroup of | #30594338, #30602455, #30602456, … |
| maximal quotient of | (C2×#6923)⋊#95, #30595321, #30595324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19683);