Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #1906 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14519749 |
| commutator | C2×C4×C61 | C22×C4 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#575 | C2 |
| socle | C2×C61 | #386 |
| hypercenter | #575 | D61 |
| hypocenter | C61 | #1906 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #575 | |
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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=df,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^60,d^b=dg,e^b=eg,f^b=fg,h^b=h^60,d^c=dg,e^c=eg,f^c=fg692 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1906, C2×#21446322, #29681924, … |
| maximal normal subgroup of | D61×#1906, C2×#21446322, #29681924, … |
| maximal quotient of | #29575482, #29575489, #29575496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5013);