Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C61 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#6923 |
| commutator, socle | C2×C61 | C24×C4 |
| Fitting | 2−1+4×C61 | C4 |
| hypercenter | 2−1+4 | #6923 |
| hypocenter | C61 | #3573 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 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,f^2=g,h^a=h^11,e^b=eg,d^c=dg,h^c=h^60,h^d=h^60,h^f=h^60323 conjugacy classes — view the full character table.
| maximal subgroup of | #30616912, #30616914, #30616916, … |
| maximal normal subgroup of | #30616912, #30616914, #30616916, … |
| maximal quotient of | #30625121, #30625122, #30625152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21506);