Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C61×#333 ⋊ C2 |
| Sylow | C61 ⋊ #1691 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14519750 |
| commutator | C42×C61 | C23 |
| Frattini | C42 | C22×D61 |
| Fitting | C61×#333 | C2 |
| socle | C22×C61 | #121 |
| hypercenter | #333 | D61 |
| hypocenter | C61 | #1691 |
| LCS | G ▷ C42×C61 ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #333 | |
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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=d,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^60,c^b=cf,h^b=h^60,e^c=eg,h^c=h^60593 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1691, C2×#21445321, #29662554, … |
| maximal normal subgroup of | D61×#1691, C2×#21445321, #29662554, … |
| maximal quotient of | #29573096, #29576205, #29576223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4012);