Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1649 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14519746 |
| commutator | C42×C61 | C23 |
| Frattini | C42 | C22×D61 |
| Fitting | D4×Q8×C61 | C2 |
| socle | C22×C61 | #120 |
| hypercenter | D4×Q8 | D61 |
| hypocenter | C61 | #1649 |
| LCS | G ▷ C42×C61 ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ D4×Q8 | |
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^60,d^b=df,e^b=eg,d^c=dg,e^c=eg776 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1649, C2×#21445068, #29655853, … |
| maximal normal subgroup of | D61×#1649, C2×#21445068, #29655853, … |
| maximal quotient of | #29568835, #29568841, #29568876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3759);