Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator | C2×C61 | C22×C42 |
| Fitting | C4×Q8×C61 | C4 |
| socle | C22×C61 | C23×C4 |
| hypercenter | C4×Q8 | #6923 |
| hypocenter | C61 | #2875 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
556 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 282 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=e,b^2=f,e^2=g,b^a=bg,h^a=h^11,d^c=dg,h^c=h^60,h^d=h^60,h^e=h^60368 conjugacy classes — view the full character table.
| maximal subgroup of | #30600806, #30600808, #30600810, … |
| maximal normal subgroup of | #30600806, #30600808, #30600810, … |
| maximal quotient of | #30609690, #30609718, #30609792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21082);