Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #3113 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D244 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#432 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #432 | D61 |
| hypocenter | C61 | #3113 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #432 | |
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^60,d^c=dg,f^c=fg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | #29575856, #29575858, #29576914, … |
| maximal normal subgroup of | #29575856, #29575858, #29576914, … |
| maximal quotient of | #29680072, #29683061, #29684906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 14641);